Proceedings of Sixth International Conference on Soft Computing for Problem Solving

As the web documents are raising at high scale, it is very difficult to access useful information. Search engines play a major role in retrieval of relevant information and knowledge. They deal with managing large amount of information with efficient page ranking algorithms. Still web spammers try to intrude the search engine results by various web spamming techniques for their personal benefit. According to the recent report from Internetlivestats in March (2016), an Internet survey company, states that there are currently 3.4 billion Internet users in the world. From this survey it can be judged that the search engines play a vital role in retrieval of information. In this research, we have investigated fifteen different machine learning classification algorithms over content based features to classify the spam and non spam web pages. Ensemble approach is done by using three algorithms which are computed as best on the basis of various parameters. Ten Fold Cross-validation approach is also used.

Image enhancement is an important image processing task that effectively improves the visual quality of an image. This image processing technique performs the operations on the input image in order to get an enhanced image. Histogram technique is a simple enhancement technique that leads to high degree of enhancement and reduces unnatural artifacts. In this research article, a color image enhancement algorithm for low resolution images is proposed. Also, a comparison of performance of various existing histogram enhancement techniques with the proposed algorithm is assessed using three parameters i.e. Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), and Bit Error Rate (BER). From these parameters, it has been observed that the proposed algorithm well enhances the low resolution images by preserving original hue.

With the advent of technology the past few years have seen the rise in the field of data mining. Data mining generally considered as the process of extracting the useful information by finding the hidden and the non-trivial information out of large chunks of dataset. Now here comes the role of association rule mining which forms a crucial component of data mining. Many recent applications like market basket analysis, text mining etc. are done using this approach. In this paper we have discussed the novel approach to implement the FP Growth method using the trie data structure. Tries provide a special feature of merging the shared sets of data with the number of occurrences that were already registered as count. So this paper widely gives an idea about how the interesting patterns are generated from the large databases using association rule mining methodologies.

In this paper, an optimization problem of 2-way ribbed slab or waffle square slab has been solved using a hybrid variant of self organizing migrating algorithm, C-SOMAQI. The main objective of this problem is to design a 2-way ribbed waffled slab of dimension 10 m * 10 m with optimum cost of steel as well as concrete. The design variables of 2-way ribbed waffled slab are taken as the effective depth of the slab (j), ribs width (p), the spacing between ribs (b), effective depth of ribs (d), and the area of reinforcement. Various population based techniques are available in literature to solve optimization problems. In this paper, a low population based hybrid technique C-SOMAQI has been taken to solve this problem that provides the solution at an optimum cost. To validate the claim, this problem has also been solved theoretically and a comparative analysis between these two solutions has been made. The study concludes that C-SOMAQI provides better results as compare to theoretical method.

In order to arm yourself and assess risk correctly in the cloud, carrying out investigations are necessary. Though Cloud Computing is the buzzing technology now a days, with the advent with which cloud computing is developing and providing solutions to the upcoming technologies where on the other side of it there also lies a down fall with respect to theft of data in the cloud, loss of data in the cloud which are related to forensic, these things create an distrustful relation between cloud user and cloud providers, during the past half decade cloud forensic has emerged as a challenging point that has to be solved in cloud computing, the prevailing existing solutions which were suggested at the initial stage of Cloud Forensics were satisfied at that time but those solutions cannot rule now also, due to which they are not up to the mark to give much satisfaction which there by strengthen the faith of users in cloud, and makes Cloud Service Providers to provide the services and make a path to be laid for the coming technologies to utilize the flavors of cloud computing. This paper inculcates the contents related to cloud forensic which are traced out which are being known, to be known. In this paper we have traced out the major causes of Cloud Forensics, and thrown a light on the causes and origins which are helpful for laying a success ladder for Cloud Forensic concepts, and provided relevant content which would be helpful to trace out the solutions which are causing obstacles in the field of Cloud Forensics, utilizing which one can get an overview of the challenges and if considered can definitely lead to a good solution methods which if implemented in a proper way can lead to recovery of lost data as well as to know the real cause of the effect and also in order to reduce their effect.

In optical networks the terminals are connected by higher bandwidth fibers. For effective use of bandwidth the capacity of these optical fibers is divided into several channels. Any damage to an optical fiber will affect the data communication on the associated channels ultimately results in data loss between the terminals. Therefore a survivable virtual mapping is required over the physical topology which can still connect the terminals in case of a link failure. Here popular ant colony optimization is used to determine the optimal paths in a survivable virtual topology. Simulation studies on a five node and a ten node network reveal the determination of virtual optimal path between all the nodes considering link-cost and hop-count. The computational time required to establish communication between the nodes of these networks using the real physical link and proposed virtual link are reported. It is observed that though the virtual connection take either equal or more time than the physical link, it can able to establish the connection even in case of any physical link failure.

Spectral clustering is playing a vital role in day-to-day technology in different forms since recent past. Spectral Clustering techniques are developed by using concepts of graph, algebra theories and conventional clustering methods. The theories and experiments conducted in various areas like, pattern recognition and image segmentation prove that it is having global reputation. This paper is to provide a framework for spectral clustering in different phases and its advantages when compared with traditional data clustering algorithms. In lieu of this paper, it is upgraded by intervening the inputs such as to making the bounds of clustering i.e., providing the issues through its relevance factors-produced by spectral clustering. On the other hand, some fundamental issues related to improving the quality of the output clusters are also covered. Constructing a sound similarity matrix is the most direct and efficient way to improve the quality of clusters. For building the similarity matrix sometimes we may choose the distance measures for measuring the similarity. This paper provides the issues related to improving the quality of the clusters produced by spectral clustering. We implemented spectral clustering in WEKA tool and produced the results for different similarity measures and observed how the quality of the clusters improved. For practical purpose we have used the datasets available in UCI machine library.

In this paper, particle swarm optimization (PSO) algorithm is presented for determining the optimal gains for a proportional-integral-derivative (PID) controller; which is implemented on a coupled tank control system to maintain the liquid level. Coupled tank system is a non-linear system and finds a wide application in industrial systems; and the quality of control directly affects the quality of uniform products, safety and cost. Initially, Ziegler-Nichols method has been used for the PID tuning but the method does not work perfectly due to lack of precision, long run time and lack of stability. The simulation results indicate that better performance has been obtained for the PSO tuned PID controller as compared with those obtained from GA & ZN tuned controllers. As per the results obtained in the paper, the proposed method is more effective in improving the time domain characteristics such as rise time, settling time, maximum overshoot and steady state error.

In the category of swarm intelligence based algorithms, Particle Swarm Optimization (PSO) is an effective population-based metaheuristic used to solve complex optimization problems. In PSO, global optima is searched with the help of individuals. For the efficient search process, individuals have to explore whole search space as well as have to exploit the identified search area. Researchers are continuously working to balance these two contradictory properties i.e. exploration and exploitation and have been modified the PSO in many different ways to improve its solution search capability in the search space. In this regard, incorporation of inertia weight strategy in PSO is a significant modification and after that many researchers have been developed different inertia weight strategies to improve the solution search capability of PSO. This paper presents an analysis of the developed inertia weight strategies in respect to problem-solving capability and their effect in the solution search process of PSO. The effect of 30 recent inertia weight strategies on PSO is measured while comparing over ten well known test functions of having different degree of complexity and modularity.

The exponential growth and dynamic nature of the world wide web has created challenges for the traditional Information Retrieval (IR) methods. Both issues are the imperative source of problems for locating the information on web. The crawlers expedite web based information retrieval systems by following hyperlinks in web pages to automatically download new and updated content. The web crawlers systematically traverse the web pages, and fetch the information viz. nature of the web content, hyper-links present on the web page, etc. This paper reviews and compares the meta-heuristic approaches like population based, evolutionary algorithms, and local search used for IR in web crawling. This paper reviews how these techniques has been developed, enhanced and applied.

High Efficiency Video Coding (H.265/HEVC) is the latest technology standard proposed by Joint Collaborative Team on Video Coding (JCT-VC). There are quite a few parameters for this encoder required to accomplish this goal. If a single standard configuration file is used for all genres of videos that may not maintain the optimal quality in all encoded videos. This is because every video has objects with unlike speeds of movement. Therefore, encoding factors must be customized in the most favorable way for each video separately. The work propose here is to use NSGA II for multi-objective optimization in order to find out the respective personalized encoding parameters to obtain higher Compression Ratio and Peak Signal-to-Noise Ratio (PSNR). Experiments on six QCIF videos with resolution $$176\times 144$$ and different configuration files have been performed. Results demonstrate that the proposed technique gives enhanced video compression quality. Test videos and code used in the research is available as supplement at http://bit.ly/HEVC-NSGA-II.

Low temperature industrial thermal applications like process heating involving solar thermal technology renders the usage of inexpensive air filled annuli receivers despite they are below par in thermal performance. This work is cantered around the air filled receiver system and more importantly try to assess both conventional and modified air filled annulus system using computational fluid dynamics (CFD) in terms of their performance parameters. For modification purpose, conventional receiver was fitted with thermal insulation in non-concentrating half section of receiver which is actually short of concentrated sun’s radiation. Finally it was simulated for significantly reduced circumferential temperature distribution (CTD) around the absorber and was compared with conventional air filled annulus receiver. This comparison could be supposed to serve as a means of advancement for the development of small scale solar thermal based heat producing plants.

In this paper some of the optimized wind turbine layouts in a windfarm, as presented by many authors, have been chosen as basis for further evaluation and study. The objective of most of earlier studies was to minimize cost per kW of power produced. This paper focuses from different perspective of optimization of turbine rotor diameters and hub heights to improve overall windfarm efficiency at a reduced cost. Differential Evolution (DE) algorithm is employed to optimize rotor diameters and hub heights of turbines in a windfarm.

The increasing number of services/offers in telecom domain offers more choices to the consumers. But on the other side, these large number of offers cannot be completely looked by the customer. Hence, some offers may pass unobserved even if they are useful for the particular kind of customers. To solve this issue, the usage of recommender systems in telecom sector is growing. So, there is need to notify the customer about the offers which are made on the basis of customer interests. The recommender system is based on demand or interest of consumer. In this paper we proposed a Big Data Analytics based Recommender System for Value Added Services (VAS) in case of telecom organizations so that they could gain profitability in the market by generating customer specific offers.

Image segmentation is the area of research to study the number of homogenous regions present in the image and to analyze the objects present in the image. The set of pixels belong to each object present in the image can be assigned same gray level to visualize certain characteristics. In this article, Particle Swarm Optimizer(PSO) based context sensitive thresholding technique has been presented to detect optimal thresholds present in the image automatically. The main objective behind utilization of the PSO is to demonstrate its effectiveness when applied to context sensitive thresholding technique to determine optimal thresholds of the image to be segmented. Further the results are compared with the two state-of-art thresholding techniques for image segmentation cited in literature. The achieved improvements are validated in terms of quantitative and qualitative parameters on the large dataset of images.

Brain performs the task of homeostasis, control and coordination. Many times normal functioning of brain is hampered due to blockage, tumors etc. Neurologists generally recommend MRI technique for the detection of any type of abnormality in the brain. The optimization algorithms can be used for extraction of the abnormal portion of the brain. This paper discusses about extraction of abnormal part of brain using the Jaya algorithm after preprocessing of the MRI images.

Script identification in multi-lingual text images will help in improving the efficiency of many real life applications, such as sorting, transcription of multilingual documents and OCR. In this paper, we have presented a technique for identification of three scripts, namely, Devanagari, Gurmukhi and Roman. We have identified the script of text based on statistical features, namely, zoning features; diagonal features; intersection and open end points based features; peak extent based features and combinations of these features. For classification, we have used multiple classification techniques, namely, Support Vector Machine (SVM), k-Nearest Neighbour (k-NN), and Convolutional Neural Network (CNN). The proposed strategy using CNN attains an average identification rate of 93.64%, with 5-fold cross-validation, for these three scripts when isolated offline handwritten characters of these scripts were considered.

Method noise is the residual image containing significant structural information lost during the process of denoising and can be effectively used for image restoration. In this paper, we propose an efficient two stage filtering approach using nonlocal means and method noise for the reduction of Gaussian noise from the images. In first stage, the block-based NLM is applied to obtain the denoised image and in second stage, the nonlocal similarities present in the method noise and the denoised image are used for the computation of effective weights for weighted NLM denoising. Experimental results demonstrate significant improvements in the denoising performance of the proposed approach as compared to the classical and block-based NLM approaches.

The work presented here solves rectangular packing problem in which rectangular items are packed on a rectangular stock sheet. Multiple objectives have been considered which are optimized using rectangle packing algorithm with different heuristics. A mathematical formulation has been presented to solve the problem. Computational experiments have been conducted to find the best packing layout for the problem.

In this paper, the implementation of the binary-coded Genetic Algorithm (GA) for multi-parameter retrieval through inverse analysis is demonstrated. A porous rectangular fin with constant thermo-physical parameters is investigated. The porous fin involves Fourier law of heat conduction along with natural convection and surface radiation phenomena. Due highly nonlinear phenomenon owing to the radiative effect and because of the associated complexity in the gradient evaluation, gradient-free method based on the GA has been used for unknown parameter retrieval. The analysis is done for satisfying a given temperature distribution on the fin surface generated using a well-validated forward solver based on the Runge-Kutta method. It is observed from the simulated experiments that for simultaneous multi-parameter retrieval, the GA yields multiple combinations of unknown parameters satisfying a particular distribution of temperature.

There is number of engineering design problems which are modeled as non-linear optimization problems. These problems are considered as benchmark problems for testing newly design optimization techniques. The objective of this paper is to demonstrate the effectiveness of a newly proposed constrained Laplacian Biogeography Based Optimization algorithm on three engineering design problems. The results are compared with existing efforts reported in literature. It is shown that in a majority of the cases constrained Laplacian Biogeography Based Optimization algorithm provides superior results.

Soft computing is an accumulation of procedures, which intend to adventure resistance for the defect, deception, ambiguity and incomplete truth to accomplish tractability, strength, and low arrangement cost. In this paper, a comprehensive overview of software testing based on soft computing is presented. In this survey, we try to elaborate some problems of software engineering specifically software testing and their solutions, which are based on soft computing approaches. The paper presents an overview of the usage of soft computing techniques including Neural Networks, Fuzzy Logic, Ant Colony Optimization, and Particle Swarm Optimization and Genetic algorithm in software testing.

This paper quantifies the most likely trade effects of the euro introduction using a panel data set of 29 European economies extended over the period 1994 to 2011. For this purpose, a gravity model of international trade is used. Following the recommendations of Santos Silva and Tenreyro (2006) paper [The log of gravity. Rev Econ Stat. 88 (4), 641–658], the gravity equation is estimated using Poisson pseudo-maximum-likelihood (PPML) technique. The main finding of this study is that the introduction of the euro has a small but statistically significant effect on export flows of European economies. The PPML estimates report this effect (euro effect) to be around 7%. This effect, although small, matches with the findings of the recent studies.

Software Defined Networking (SDN) is defined as a solution for security, reliability and flexibility problems in traditional networks. It decouples the data plane and control plane. SDN is a programmable approach of networking. In this technology network can be controlled by a program. The key characteristic of Software Defined Networking is that it proposes the separation of the data plane and the control plane, this control is given to a centralize controller and Open data devices are used for data forwarding. These devices can act either as switch, hub or as any other network device it depends upon the application. Those applications also can be attack mitigation applications. In our proposed work we develop an IP spoofing attack mitigation application. That application can detect and mitigate the IP spoofing attack in SDN in LAN. Here, we will use POX controller so have to develop program in python language. The emulation tool Mininet is used for experiment.

This investigation is concerned with the performance prediction and admission control F-policy for the machine repair problem with retrial. To develop a Markov model, the steady state Chapman-Kolmogorov equations are constructed. The system state probabilities are obtained by using recursive method. Various performance measures are established explicitly in terms of steady state probabilities. To examine the effects of system parameters, the numerical simulation is performed by choosing a suitable illustration. The cost function is also framed to evaluate the optimal service rate and corresponding optimal cost. ANFIS soft computing technique is used to compare the numerical results obtained analytically and also by implementing ANFIS.

Rainfall induced landslides account for over 200 deaths and loss of over Rs.550 crores annually in Himalaya. Literature suggests sensors based site specific Early Warning System (EWS) to be feasible and economic to curtail losses due to landslides for high risk areas. Area selected for current study is Tangni landslide located in Chamoli district of Uttarakhand state, India due to high anticipated risk to the local community residing nearby. For realization of EWS, a near real time instrumentation setup was installed on the slope. The setup measures pore water pressure, sub-surface deformations, and surface displacements along with rainfall. Regression analysis models are developed using antecedent rainfall and deformation data which are further used to find out thresholds for sensors based on z-scores. In future using the results from the sensors installed in the field and laboratory characterizations, numerical analyses will be applied to develop a process based model.

Security in banking transactions is major concern. In this paper we propose a method to use face as a biometric password along with PIN number in ATM machines. For face recognition in controlled environment Wavelet, LBP and PCA are used. This can be used to perform more secure ATM transactions. Even after authorizing the access to a user the algorithm continuously monitors the user. If a user chooses to leave the ATM machine without completing his/her ongoing transaction or moves his/her head away from the camera for 10 s then his/her session will be logged out automatically and he/she will have to restart a new transaction. Our technique can easily be combined with regular ATM machines and people do not even require any further knowledge to use ATM machines. This technique can also be combined with banking websites to provide more safe and secure online transactions for online users.

In this paper, support vector machines with combinations of different feature selection and extraction techniques are used for the prediction of defective software module. It is tested on five NASA datasets. Correlation-based feature selection technique (CFS), principal component analysis (PCA) and kernel principal component analysis (KPCA or kernel PCA) techniques are used for feature selection and feature extraction. It has been shown that the CFS + SVM gives better prediction results and accuracy compare to PCA + SVM and KPCA + SVM.

In this investigation, the single server retrial queue is studied under the assumption that the arrival of the positive customers occur in bulk with state dependent rates. The server may breakdown during the essential and optional services due to arrival of negative customers. The combined supplementary variable and generating function approach is used to analyze the mathematical model and to find the queueing characteristics. The cost function has been constructed to determine the optimal number of parameters involved for providing the desired efficiency to the system. The numerical results for various performance indices are presented to examine the system behavior. The Adaptive Neuro Fuzzy Inference System (ANFIS) technique which is the combination of neural network and fuzzy logic has been used to design a fuzzy inference model for the retrial queueing system. The neuro fuzzy based numerical results are generated for the mean queue length.

This paper presents how humans trained in primitive haptic based patterns using a wearable sleeve, can recognize their scaling and shifting. The wearable sleeve consisted of 7 vibro-actuators to stimulate subjects arm to convey the primitive haptic based patterns. The focus of this study to understand (1) whether the human somatosensory system uses primitive patterns that can be modeled using Gaussian like functions to represent haptic perceptions, (2) whether these primitive representations are localized (cannot be shifted along the skin) and magnitude specific (cannot be scaled). These insights will help to develop more efficient haptic feedback systems using a small number of templates to be learnt to encode complex haptic messages.

Distribution of work load (job) among the virtual machine is one of the challenging issues in cloud environment. It is very difficult to predict the execution time of job in cloud computing. So Cloud job scheduler should be dynamic in nature and distribute the job among the virtual machine in such a manner, no virtual machine should be in overloaded or ideal condition. We proposed an algorithm considering the priority of jobs and cost of resource. Job priority and cost of resources is major issue to establish a cloud environment for enterprises. For better quality of service and utilization of resources IBA algorithm is suited for this purpose. Result shows that IBA minimize the idle time of resources but IBA does not provide the guarantee for handling job priority and cost of the resource. So there is a need of job scheduling algorithm that considers job priority and recourse cost.

Solar energy is abundantly available on earth. The temperature of heat source needs to be high for the higher efficiency; be it energy production through thermodynamic cycle or heat extraction using heat transfer media, and solar energy concentration devices helps in achieving high temperature. Parabolic trough collector (PTC) has its own advantage with concentration ratio upto 215 times with reasonable cost and operational convenience, especially when low to medium range temperature heating is required. Present work is focused on the experimental and computational study on PTC with different heat transfer fluids towards identifying a suitable heat transfer fluid and flow parameters towards achieving higher heat collection and transfer efficiency. Most decisive thermo-physical entity such as heat transfer fluid (HTF) and its property i.e. flow rate is varied and its influence on the thermal efficiency, heat transfer and net effective temperature gain is analysed with the numerical model and results validated with experimental work. For numerical study, computational fluid dynamics (CFD) approach is taken using ANSYS–fluent software package. The experimentation results are in good agreement with the numerical model and suggest that with the flow rates of different HTF maintained within 3–5 LPM, the temperature gain can be achieved between 3–6 °C in a single pass with a maximum efficiency of 59.7%.

Retinal blood vessels are linked with hypertension and cardiovascular disease. It is generally known that vascular bifurcation is mainly involved in varying blood flow velocity as well as its pressure. This paper presents an efficient method for automatic location of blood vessel bifurcations in digital eye fundus images. The proposed algorithm comprised of three main steps: image enhancement, fuzzy clustering, and searching vascular bifurcation. The purposed algorithm revealed successful detection of bifurcations upon test images. Results showed improved diagnostic accuracy in identifying bifurcations with use of the proposed algorithm and encourage its use for further applications such as image registration, personal identification and pre-clinical scanning of retina diagnosis.

Lingo© is a basic programming tool for solving linear programming problems (LPPs), non-linear programming problems (NLPPs) and other related programming problems. But this software has certain limitations like it can not be employed on complex hierarchical programming problems like bi-level programming problems (BLPPs), multi-level programming problems (MLPPs) etc. In this context researchers namely Kuo and Huang [1] have presented a method based on particle swarm optimization (PSO) algorithm for solving bi-level programming problems and performance of developed method have been analysed with the results of other methods like fuzzy neural networks (ANN), genetic algorithm (GA), lingo (software) on same numerical examples. In this article, the feasibility of Lingo© software for solving bi-level linear programming problems (BLPPs) has been studied and proved that this software cannot be used for solving BLPPs. The aim of this paper is to identify the results and performance analysis given by Kuo and Huang with Lingo are incorrect and Lingo© is not feasible for solving bi-level linear programming problems (BL-LPPs).

The purpose of this research is to find a best fitting model to predict the electricity consumption in a health care institution and to find the most suitable forecasting period in terms of monthly, bimonthly, or quarterly time series. The time series data used in this study has been collected from a health care institution Apollo Hospital, Ludhiana for the time period of April 2005 to February 2016. The analysis of the time series data and prediction of electricity consumption have been performed using ARIMA (Autoregressive Integrated Moving Average) model. The most suitable candidate model for the three time series is selected by considering the lowest value of two relative quality measures i.e. AIC (Akaike Information Criterion) and SBC (Schwarz Bayesian Criterion). The appropriate forecasting period is selected by considering the lowest value of RMSE (Root Mean Square Error) and MPE (Mean Percentage Error). After building the final model a two-year prediction of electricity consumption of the health care institution is performed.

In today’s world Artificial intelligence (AI) is known for deploying human like intelligence in to computers, so that they behave like humans. One of specialization areas of AI is expert systems. This area focuses on programming machines to take real life decisions. System with its intelligence helps users by suggesting them with variety of choices and making it easier for people to take best decisions while purchasing items. This work is intended to develop and deploy a Hotel Recommendation System. The work makes use of Collaborative user and item filtering techniques in combination with sentiment classification for generating recommendations. To improve the recommendations results, sentiment classification results are used as the feedback. There is also performance comparison between two different classifiers “Naïve Bayesian” (NB) and “K-Nearest Neighbor” (K-NN) with respect to their ability to recommend. This hybrid technique helps us in the case where an item has no ratings but has only textual reviews. Since this technique draws conclusion based on reviews along with the ratings, recommendation results are more accurate compared to recommendation systems based solely on filtering techniques.

Natural Language Processing (NLP) is a technique used to build computational models which deals with the interaction between computers and human languages. Question answering is expected to give the precise results for the query instead of a group of links or references which might contain an answer. The information in the web is basically growing and users are finding difficult to look for the answers through the search engines. In this research, a new approach is used to build the question answering system which uses vector space model by using unstructured data. In this proposed work, Keywords are generated by calculating the tf-idf score for each keyword and they are indexed to every file and query. The query vectors and Document vectors are compared and similarity values are generated using term frequency. Highest ranked documents are generated as per the similarity values and NER tagging is done to produce candidate answers from which best answer is chosen.

This article discusses delayed model of HIV infection with combination therapy consisting of RTI and PI drug. The delay included in this article two kinds of delays viz. immune response delay and intracellular delay. A well known growth law so called logistic growth is assumed for uninfected and healthy T cell. Local properties of the infection free equilibrium point is discussed in terms of $$R_0$$, the basic reproduction number. The existence of Hopf bifurcation with respect to delayed parameter is verified using geometric switching conditions numerically because of delay dependent parameters in the model. Extensive numerical simulations have been carried out on the model to ascertain the effects of drug on viral dynamic and disease progression.

In the present work, we examine the three-point numerical scheme for the non-linear second order ordinary differential equations having integral form of forcing function. The approximations of solution values are obtained by means of finite difference scheme based on a special type of non-uniform meshes. The derivatives as well as integrals are approximated with simple second order accuracy both on uniform meshes and non-uniform meshes. A brief convergence analysis based on irreducible and monotone behaviour of Jacobian matrix to the numerical scheme is provided. The scheme is then tested on linear and non-linear examples that justify the order and accuracy of the new method.