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This special volume of the conference will be of immense use to the researchers and academicians. In this conference, academicians, technocrats and researchers will get an opportunity to interact with eminent persons in the field of Applied Mathematics and Scientific Computing. The topics to be covered in this International Conference are comprehensive and will be adequate for developing and understanding about new developments and emerging trends in this area. High-Performance Computing (HPC) systems have gone through many changes during the past two decades in their architectural design to satisfy the increasingly large-scale scientific computing demand. Accurate, fast, and scalable performance models and simulation tools are essential for evaluating alternative architecture design decisions for the massive-scale computing systems. This conference recounts some of the influential work in modeling and simulation for HPC systems and applications, identifies some of the major challenges, and outlines future research directions which we believe are critical to the HPC modeling and simulation community.

Inhaltsverzeichnis

Frontmatter

Mathematical Modeling, Applications, and Theoretical Foundations

Frontmatter

Canonical Duality-Triality Theory: Unified Understanding for Modeling, Problems, and NP-Hardness in Global Optimization of Multi-Scale Systems

A unified model is addressed for general optimization, topology design, and control problems in multi-scale complex systems. Based on necessary conditions and fundamental principles in physics, a unified canonical duality theory is presented in a precise way to include traditional duality theories and popular methods as special applications. The well-known quadratic/linear knapsack problems are solved analytically in terms of its canonical dual solutions. Both uniqueness and existence are proved. Two conjectures on NP-hardness are discussed, which play important roles for correctly understanding and efficiently solving challenging real-world problems. Applications are illustrated for nonconvex continuous optimization, d.c. programming, fixed point problems, mixed integer nonlinear programming, bilevel optimization, and engineering design and control. Misunderstandings and mistakes on some basic concepts, such as objectivity, nonlinearity, Lagrangian, and Lagrange multiplier method are discussed and classified. This paper will bridge a significant gap between optimization and multidisciplinary fields of applied mathematics, engineering physics, and computational sciences.

David Gao

Numerical Investigation of Stochastic Neural Field Equations

We introduce a new numerical algorithm for solving the stochastic neural field equation (NFE) with delays. Using this algorithm, we have obtained some numerical results which illustrate the effect of noise in the dynamical behaviour of stationary solutions of the NFE, in the presence of spatially heterogeneous external inputs.

Pedro M. Lima

Nonstationary Signal Decomposition for Dummies

How can I decompose a nonstationary signal? What are the advantages of using the most recent methods available in the literature versus using classical methods like (short time) Fourier transform or wavelet transform? This paper tries to address these and other questions providing the reader with a brief and self-contained survey on what and how to tackle the decomposition of nonstationary signals.

Antonio Cicone

Modeling the Socio-Economic Waste Generation Factors Using Artificial Neural Network: A Case Study of Gurugram (Haryana State, India)

Municipal solid waste management is a serious environmental issue concerning developed as well as developing countries worldwide. A successful waste management system requires accurate planning as well as waste generation and collection prediction data with precision. A number of socio-economic factors are responsible for generation of municipal solid waste. In this study the socio-economic factors (such as population, urban population, literate population, and per capita income) have been identified which are responsible for generation of municipal solid waste in Gurugram district (Haryana State, India). In this research work artificial neural network models have been developed (1) to predict the collected municipal solid waste of Gurugram district for five years (2017–2021) and (2) to observe the socio-economic factors effect individually and collectively on waste collection of Gurugram district. The results have been validated by minimum value of mean squared error and maximum value of coefficient of correlation R between observed and predicted municipal solid waste. The artificial neural network model based on individual factor per capita income has shown highest coefficient of correlation R (0.89) (between observed and predicted municipal solid waste) and least value of mean squared error (0.036). The artificial neural network model based on all the factors such as population, urban population, literate population, and per capita income has shown highest coefficient of correlation R (0.915) and least value of mean squared error (0.029). It is observed that expected collected waste by sanitation worker of Municipal Corporation of Gurugram would be approximately 1247096.43 Metric tons within period 2017–2021 and expected generated waste would be approximately 1781566.32 Metric tons within period 2017–2021. It is expected that the proposed research work will be helpful for the authorities of Municipal Corporation of Gurugram.

Ajay Satija, Dipti Singh, Vinai K. Singh

Regularization of Highly Ill-Conditioned RBF Asymmetric Collocation Systems in Fractional Models

While attempting to approximate differential equations using Kansa’s radial basis function (RBF) collocation, we need to solve a non-symmetric, highly ill-conditioned system. There are many attempts to evaluate RBF interpolant in a more stable manner using approaches like Laurent series expansion, regularization, QR algorithms, etc. In this article, we modify the regularization method and obtain regularization parameter that reduces the ill-conditioning and provide stable solutions for fractional differential equations using Kansa’s asymmetric collocation. Numerical results are provided to illustrate the algorithm.

K. S. Prashanthi, G. Chandhini

The Effect of Toxin and Human Impact on Marine Ecosystem

We formed a plankton-nutrient interaction model which consists of phytoplankton, herbivorous zooplankton, dissolved limiting nutrient with general nutrient uptake functions, instantaneous nutrient recycling, and harvesting on plankton population. Afterward, we modified and expanded the primary model by considering the effect of sunlight, additional nutrients, harmful chemicals, and carbon dioxide into account. Phytoplankton obtain carbohydrate supply from the carbon dioxide in the air, and the overall nutrient uptake rate increases in the presence of sunlight. So, the effect of sunlight and additional food is discussed. Hypothetically, carbon dioxide accelerates the growth of phytoplankton but we considered some limiting factors which abate the process. Some assumptions were made to construct the system equations. We assumed that phytoplankton releases toxic substances to defend themselves from the predation of zooplankton. The entire system was studied analytically, and the threshold values for the existence and stability of various steady states were discussed. Further, we discussed whether pollution emissions can variate the dynamics of the primary system, bring in recurrence bloom therein toxic phytoplankton can be applied to a great extent to sustain system stability.

S. Chakraborty, S. Pal

A Computational Study of Reduction Techniques for the Minimum Connectivity Inference Problem

The minimum connectivity inference (MCI) problem is an NP-hard discrete optimization problem. Its description is based on a simple, undirected, and complete graph given by a vertex set. Moreover, a finite number of clusters (subsets of the vertex set) are given. These clusters may overlap each other. The problem consists in determining an edge set with minimal cardinality so that the vertices in each cluster are connected by edges of this set which have both vertices in the cluster. Research on the MCI problem can be traced back from 1976 to the present and includes complexity results, reduction techniques, heuristic solution approaches, and various applications. Some years ago, the MCI problem has been modeled as a mixed integer linear programming (MILP) problem which enables to solve MCI instances exactly up to a small size. An improved MILP formulation, recently introduced by the authors of the present contribution, allows for successfully tackling moderately sized instances. To further increase the size of MCI instances that can be solved exactly (or to reduce the required computation time), reduction techniques can be very helpful. Such techniques aim at converting a given instance into an instance with fewer clusters or vertices or both. Our contribution will briefly review the improved MILP-based solution approach as well as reduction techniques. Based on this, we will present a computational study on the influence of several reduction techniques on the problem size and the computation time. In addition, we will also discuss the effect of a heuristic reduction technique.

Muhammad Abid Dar, Andreas Fischer, John Martinovic, Guntram Scheithauer

Approximate Controllability of Nonlocal Impulsive Stochastic Differential Equations with Delay

This paper concerns with the approximate controllability of nonlocal impulsive stochastic differential equations with delay in Hilbert space setting. Using stochastic analysis and fixed point approach, a new set of sufficient conditions is formulated that guarantees the approximate controllability of the considered stochastic system. To show the effectiveness of the developed theory, an example is constructed.

Surendra Kumar

Convergence of an Operator Splitting Scheme for Abstract Stochastic Evolution Equations

In this paper, we study the convergence of a Lie-Trotter operator splitting for stochastic semilinear evolution equations in a Hilbert space. The abstract Hilbert space setting allows for the consideration of convergence of the approximation for both the original and spatially discretized problems. It is known that the strong convergence of this scheme is classically of half-order, at best. We demonstrate that this is in fact the optimal order of convergence in the proposed setting, with the actual order being dependent upon the regularity of noise collected from applications.

Joshua L. Padgett, Qin Sheng

Modified Post-Widder Operators Preserving Exponential Functions

The paper considers a modification P ˜ n $$\widetilde {P}_n$$ of the Post-Widder operators, which contains two auxiliary functions a n(x), b n(x). The main result consists of the conclusion that under an appropriate choice of a n(x), b n(x), the operator P ˜ n : C [ 0 , ∞ ) → C [ 0 , ∞ ) $$\widetilde {P}_n: C[0,\infty )\to C[0,\infty )$$ has two eigenfunctions exp(c i x) associated with the same unit eigenvalue. Here, c 1 < c 2 are real numbers. We establish direct estimates, including a quantitative asymptotic formula for the modified form of the operators. Finally, we represent the error graphically using the software Mathematica.

Vijay Gupta, Vinai K. Singh

The Properties of Certain Linear and Nonlinear Differential Equations

We consider linear differential equations of the second- and the third-order and nonlinear second-order differential equations related via the Schwarzian derivative. The main objective of the paper is to obtain relations between the solutions of the second- and the third-order linear differential equations and the solutions of the nonlinear differential equations of the second order. The method is based on the use of the Schwarzian derivative, which is defined as the ratio of two linearly independent solutions of the linear differential equations of the second and the third order. As a result, we obtain new relations between the solutions of these linear and nonlinear equations.

Galina Filipuk, Alexander Chichurin

Fixed Points for (ϕ, ψ)-Contractions in Menger Probabilistic Metric Spaces

In this paper, we work out a fixed point result for weakly contractive mapping in Menger probabilistic metric space. A combination of analytic and order theoretic approach is used to establish our main theorem. The main result is illustrated with an example.

Vandana Tiwari, Tanmoy Som

A Novel Canonical Duality Theory for Solving 3-D Topology Optimization Problems

This paper demonstrates a mathematically correct and computationally powerful method for solving 3D topology optimization problems. This method is based on canonical duality theory (CDT) developed by Gao in nonconvex mechanics and global optimization. It shows that the so-called NP-hard knapsack problem in topology optimization can be solved deterministically in polynomial time via a canonical penalty-duality (CPD) method to obtain precise 0-1 global optimal solution at each volume evolution. The relation between this CPD method and Gao’s pure complementary energy principle is revealed for the first time. A CPD algorithm is proposed for 3-D topology optimization of linear elastic structures. Its novelty is demonstrated by benchmark problems. Results show that without using any artificial technique, the CPD method can provide mechanically sound optimal design, also it is much more powerful than the well-known BESO and SIMP methods. Additionally, computational complexity and conceptual/mathematical mistakes in topology optimization modeling and popular methods are explicitly addressed.

David Gao, Elaf Jaafar Ali

High Performance and Scientific Computing

Frontmatter

High Performance Computing: Challenges and Risks for the Future

In this paper, we describe the challenges that high performance computing (HPC) is facing and will be facing over the coming years. We will look into the challenges that HPC faces with the coming end of Moore’s law. We will look into the opportunities we see in software and algorithms. Finally, we will discuss the convergence of HPC and data analytics. We will conclude by pointing at the new challenges and opportunities that arise from this convergence.

Michael M. Resch, Thomas Boenisch, Michael Gienger, Bastian Koller

Modern Parallel Architectures to Speed Up Numerical Simulation

Applications of graphics processing units (GPU) and field programmable gate array (FPGA) for computer codes acceleration are discussed. Most of the high positions in the top-100 list of supercomputers (clusters) are taken by a hybrid type hardware. First, the authors provide an idea about GPU and FPGA architectures. The use of FPGA has two main obstacles, involving the necessity for manual coding of algorithms up to the register transfer level (RTL). So, modern high level synthesis (HLS) technology to use FPGA is briefly introduced. Then several examples of speeding up algorithms mostly from the Earth Sciences are given. The considered examples of GPU use are: decomposition of seismic records by wave packages (performance gain of 350 times is achieved); the convolution problems with Green’s function (the computation time at single GPU is 162 times faster than the original code version); and tsunami wave propagation (simulation of tsunami wave propagation was accelerated 100 times compared to one CPU). In some cases FPGA shows even better results compared to GPU, in particular for tsunami modelling (five times faster than compared even to GPU Tesla K40), HD video stream processing. As for FPGA-based data processing, the following examples are here considered: searching for small objects on a series of images; searching object on the image; and motif search in DNA sequence. In all cases comparison with one CPU is given.

Mikhail Lavrentiev, Konstantin Lysakov, Alexey Romanenko, Mikhail Shadrin

Parallel Algorithms for Low Rank Tensor Arithmetic

High-dimensional tensors of low rank can be represented in the hierarchical Tucker format (HT format) with a complexity which is linear in the dimension d of the tensor. We developed parallel algorithms which perform arithmetic operations on tensors in the HT format, where we assume the tensor data to be distributed over several compute nodes. The parallel runtime of our algorithms grows like log ( d ) $$\log (d)$$ with the tensor dimension d, due to the tree structure of the HT format. On each of the compute nodes one can use shared memory parallelization to accelerate the algorithms further. One application of our algorithms is parameter-dependent problems. Solutions of parameter-dependent problems can be approximated as tensors in the HT format if the parameter dependencies fulfil some low rank property. Our algorithms can then be used to perform post-processing on solution tensors, e.g., compute mean values, expected values or other quantities of interest. If the problem is of the form Ax = b with the matrix A as well in the HT format, we can compute the residual of a solution tensor or even compute the entire solution directly in the HT format by means of iterative methods.

Lars Grasedyck, Christian Löbbert

The Resiliency of Multilevel Methods on Next-Generation Computing Platforms: Probabilistic Model and Its Analysis

The reduced reliability of next-generation exascale systems means that the resiliency properties of a numerical algorithm will become an important factor both in the choice of algorithm and in its analysis. The multigrid algorithm is the workhorse for the distributed solution of linear systems but little is known about its resiliency properties and convergence behavior in a fault-prone environment. In the current work, we propose a probabilistic model for the effect of faults involving random diagonal matrices. We summarize results of the theoretical analysis of the model for the rate of convergence of fault-prone multigrid methods which show that the standard multigrid method will not be resilient. Finally, we present a modification of the standard multigrid algorithm that will be resilient.

Mark Ainsworth, Christian Glusa

Visualization of Data: Methods, Software, and Applications

Visualization is a part of data science, and essential to enable sophisticated analysis of data. The visualization ensures the human participation in most decisions when analyzing data. In this paper, we review methods and software for visualization of multidimensional data. The emphasis is put on the web-based DAMIS solution for data analysis, allowing researchers to carry out the primary data analysis and to investigate the projection of multidimensional data on a plane, the similarities between the data items, the influence of individual features, and their relationships by visual analysis techniques, using the high-performance computing resources. DAMIS is applied to the visual efficiency analysis of regional economic development to evaluate how regional resources are reflected in the economic results. The projection methods (principal component analysis, multidimensional scaling) and artificial neural networks (self-organizing map, SAMANN) are the core strategies for the analysis.

Gintautas Dzemyda, Olga Kurasova, Viktor Medvedev, Giedrė Dzemydaitė

HPC Technologies from Scientific Computing to Big Data Applications

Recent advances in information technology and its widespread growth in the areas of business, engineering, medical and scientific studies have resulted in information explosion. High performance computing (HPC) systems are essential for solving scientific problems involving massive data using high computation power and high throughput networks. Due to the widespread growth of data in various fields, knowledge discovery and decision making is a challenging task and has resulted in the emerging trend of Big Data analytics. Big data is related to complex, diverse and massive data sets comprising of structured, semi-structured and unstructured data. Such data cannot be processed and analysed with the traditional database technologies. HPC systems can be extended to Big data applications for large-scale processing and analysis thus shifting the paradigm from traditional scientific computing domain to data intensive domain or Big data. The aim of this paper is to present an overview of the evolution and principles starting from scientific computing to present Big Data analytics.

L. M. Patnaik, Srinidhi Hiriyannaiah

Models, Methods, and Applications Based on Partial Differential Equations

Frontmatter

Analysis and Simulation of Time-Domain Elliptical Cloaks by the Discontinuous Galerkin Method

In this paper, we first give a quick review of the current status of the invisibility cloak with metamaterials. Then, we focus on the elliptical cloak model and establish its stability. Finally, we develop a discontinuous Galerkin method and demonstrate its effectiveness in reproducing the cloaking phenomena originally simulated by the edge element method.

Yunqing Huang, Chen Meng, Jichun Li

Dynamic Pore-Network Models Development

A two-pressure dynamic drainage algorithm is developed for three-dimensional unstructured network model. The impact of time step is discussed through drainage simulations. Dynamic effects in average phase pressure for fluid phases with different viscosity ratios are explored using the developed code as an upscaling tool. For cases where two fluids have significant viscosity differences, the viscous pressure drop within one fluid may be neglected. This dynamic algorithm can then be simplified into a single-pressure one. This simplification has been done for both drainage and imbibition. Saturation patterns during imbibition for different boundary pressure drops are studied. With the increase of boundary pressure, invasion becomes less capillary dominant with a sharper wetting front.

X. Yin, E. T. de Vries, A. Raoof, S. M. Hassanizadeh

Mean Field Magnetohydrodynamic Dynamo in Partially Ionized Plasma: Nonlinear, Numerical Results

A magnetohydrodynamic dynamo operating in partially ionized surface and atmospheric layers of stars can produce variety of magnetic field structures. In partially ionized plasma such as in the solar photosphere and the solar chromosphere, the magnetic induction equation is subjected to the Hall drift and the ambipolar diffusion (arising due to ion-neutral collisions) along with the Ohmic dissipation. It has been found out that in the presence of a shear flow, the Hall and the ambipolar diffusion, magnetic field components can grow rapidly to form the horizontal structures with small spatial scales. The effects of nonlinear dynamo, along with a shearing flow, Hall drift, ambipolar diffusion and the density gradient can play an important role in the evolution of magnetic field in the partially ionized surface layers of cool stars.

K. A. P. Singh

Outcome of Wall Features on the Creeping Sinusoidal Flow of MHD Couple Stress Fluid in an Inclined Channel with Chemical Reaction

A mathematical model has been developed with an aim to study the dispersion of a solute substance of an incompressible MHD couple stress fluid in an inclined channel with peristalsis and wall features in the presence of heterogeneous-homogeneous chemical reactions. Following Taylors approach, the resulting equations are solved analytically by long wavelength approximation, and the expression for diffusion coefficient is obtained. It is found that inclination of the channel and wall features favor the dispersion but magnetic and couple stress constraints resist the dispersion.

Mallinath Dhange, Gurunath Sankad

A Fractional Inverse Initial Value Problem

We are concerned with an inverse problem associated with a one-dimensional fractional parabolic equation in the impedance form. The spectral data is extracted from a single reading of the values of a solution collected on the boundaries. The mathematical tools are drawn from M.G. Krein’s inverse spectral theory of the string, and the use of a classical initial condition makes it appropriate for imaging by nondestructive methods.

Amin Boumenir, Vu Kim Tuan

Three-Dimensional Biomagnetic Flow and Heat Transfer over a Stretching Surface with Variable Fluid Properties

In this study, we investigate the effects of variable fluid properties on the flow and heat transfer of three-dimensional biomagnetic fluid over a stretching surface in the presence of a magnetic dipole. In our model, we assume that the fluid viscosity and thermal conductivity vary with temperature and the wall temperature varies in the (x, y) plane. The model used also takes into account magnetization and electrical non-conductivity, which is described by the principle of ferrohydrodynamics. The governing equations are transformed into a system of ordinary differential equations by using similarity transformations and solved numerically using the essential features of this technique. It is based on: (i) the common finite difference method with central differencing; (ii) a tridiagonal matrix manipulation; and (iii) an iterative procedure. The influence of various parameters, namely the viscosity parameter, the thermal conductivity parameter, the ferromagnetic interaction parameter, on the velocity and temperature fields is analyzed and presented graphically. This results analysis shows that the magnetic force and viscosity control the fluid behavior and the friction coefficient. The accuracy of the numerical result compares with previously published work and the results are found to be in good agreement

M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Effects of Slip on the Peristaltic Motion of a Jeffrey Fluid in Porous Medium with Wall Effects

Peristaltic stream of Jeffrey fluid is considered in a permeable channel having wall properties to analyze the slip effects underneath the presumptions being small Reynolds number and large wavelength. Time average velocity and stream function are obtained mathematically. The motion is examined referring the fixed frame and transmitting with constant speed along the frame. The flow is examined to analyze the results of various parameters. The influence of Jeffrey parameter, permeability parameter, slip parameter, and elastic parameters is discussed and shown graphically.

Gurunath Sankad, Pratima S. Nagathan

Linear and Nonlinear Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Layer with Soret Effect and Internal Heat Source

In this paper, we analyze the effect of internal heating and the Soret effect on linear and nonlinear double diffusive convection in a couple stress fluid saturated anisotropic porous layer, heated and salted from below. Linear stability analysis has been performed by using normal mode technique and nonlinear analysis is carried out using a truncated Fourier series. The modified Darcy model, which includes the time-derivative term, has been employed in the momentum equation. The effects of the Vadasz number, the anisotropic parameter, the Soret parameter, the couple stress parameter, the solute Rayleigh number, the internal heat source parameter, the Lewis number, the Darcy–Prandtl number, and normalized porosity on the stationary and oscillatory are shown graphically. Also, heat and mass transports are calculated in terms of the Nusselt number and the Sherwood number and shown graphically.

Kanchan Shakya

Modeling of Wave-Induced Oscillation in Pohang New Harbor by Using Hybrid Finite Element Model

Harbors are designed to provide the safe loading, unloading, and sheltering for the moored vessels as this region experiences high oscillations due to combined effect of wave refraction, diffraction, and partial reflection from the solid harbor walls. An accurate description of the mathematical model is required, to analyze the wave-induced excitation in the harbor. The fluid domain is divided into two regions as bounded and open sea region. Firstly, the mild-slope equation (MSE) is derived for both regions in terms of a potential function using the energy conservation principle. The total wave energy in the bounded region is estimated by using the hybrid finite element method (HFEM), which is used to formulate the mild-slope equation. In HFEM model, the finite element method is coupled with the analytical approximation method to solve the mild-slope equation in both regions. The present HFEM model is utilized to analyze the convergence behavior for the rectangular harbor. Further, the present numerical scheme is implemented on realistic Pohang New Harbor (PNH) situated in Pohang city (Korea) to analyze the regions of strong and weak amplification. The current numerical model is implemented on regular- and irregular-shaped ports or harbors and can be used as an efficient engineering tool for planning and designing of the artificial industrial harbor and prediction of the incident wave response under the resonance condition.

Prashant Kumar, Rupali, Rajni

Similarity Solution of Hydromagnetic Flow Near Stagnation Point Over a Stretching Surface Subjected to Newtonian Heating and Convective Condition

Two-dimensional steady boundary layer flow of an incompressible electrically conducting fluid near a stagnation point region over a stretching surface with Newtonian heating and convective boundary condition in the presence of magnetic field is carried out. Governing nonlinear partial differential equations are reduced into a system of nonlinear ordinary differential equations with the aid of suitable similarity transformations. Numerical solutions of transformed boundary layer equations are clarified by using perturbation technique for small magnetic parameter. Several parameters such as stretching parameter, magnetic parameter, conjugate parameter, and Prandtl number, determining the velocity and temperature profiles, are displayed through graphical representation. Furthermore, impact of controlling parameters on local skin friction coefficient and local Nusselt number is also computed and presented in tabular form. Computational results of shear stress are compared with the previous published works.

KM Kanika, Santosh Chaudhary, Mohan Kumar Choudhary

Modelling Corrosion Phenomenon of Magnesium Alloy AZ91 in Simulated Body Fluids

Magnesium alloy AZ91 is one of the best suited biodegradable biomaterials for bioimplants. Magnesium is a highly active metal with accelerated corrosion in physiological environments. AZ91 alloy has two distinct phases in the matrix, which form galvanic couple inducing micro galvanic corrosion (primary phase anodic with respect to the secondary phase) in the alloy. However, the corrosion rate could be controlled by tailoring the microstructure of the alloy. The distribution and dispersion of secondary phase particles greatly influence the corrosion rate of the material. A numerical model was developed using Comsol Multiphysics® to study the effect of distribution of secondary phase on the corrosion rate of the alloy. The average anodic current density was found to be higher for AZ91 with continuous network secondary phase microstructural configuration. The average anodic corrosion current and the corrosion rate were found to be lower for AZ91 with dispersed secondary phase microstructural configuration. The numerical modelling results were found to be consistent with the experimental results available in the literature.

Ramalingam Vaira Vignesh, Ramasamy Padmanaban

Approximate and Analytic Solution of Some Nonlinear Diffusive Equations

Nonlinear partial differential equations (PDEs) have wide range of applications in mathematics, science and engineering and are used in modelling various types of problems arising in fluid mechanics. This paper presents the numerical approximation of some nonlinear diffusive PDEs; Newell–Whitehead–Segel (NWS) equation and Burgers’ equation by using Laplace decomposition method (LDM) and finite difference method(FDM). The nonlinear PDEs are considered to study the influence of the parameters like initial condition and dissipative coefficient on the solution, wave distortion, and wave propagation. The numerical results obtained are analysed graphically. The approach can be extended to obtain physically relevant solutions to a wide range of nonlinear PDEs describing various real life phenomena involving nonlinear and dissipative effects. MATLAB-R2017b is used for all the computations and graphical representation.

Amitha Manmohan Rao, Arundhati Suresh Warke

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