Top

Neural Computing and Applications

Published in:

01-04-2016 | Original Article

An exponential approach for the system of nonlinear delay integro-differential equations describing biological species living together

Authors: Şuayip Yüzbaşı, Mehmet Sezer

Published in: Neural Computing and Applications | Issue 3/2016

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper, we consider a system of nonlinear delay integro-differential equations with convolution kernels, which arises in biology. This problem characterizes the population dynamics for two separate species. We present an exponential approach based on exponential polynomials for solving this system. This technique reduces the model problem to a matrix equation, which corresponds to a system of nonlinear algebraic equations. Also, illustrative examples related to biological species living together are given to demonstrate the validity and applicability of technique. The comparisons are made with the existing results.

previous article A novel integral extension LMD method based on integral local waveform matching

next article Online classifier adaptation for cost-sensitive learning

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Kot M (2001) Elements of mathematical ecology. Cambridge University Press, CambridgeCrossRefMATH

Pougaza D-B (2007) The Lotka integral equation as a stable population model. Postgraduate Essay, African Institute for Mathematical Sciences (AIMS), Muizenberg

Kopeikin ID, Shishkin VP (1984) Integral form of the general solution of equations of steady-state thermoelasticity. J Appl Math Mech (PMM U.S.S.R.) 48(1):117–119MathSciNetCrossRefMATH

Lotka AJ (1939) On an integral equation in population analysis. Ann Math Stat 10:144–161CrossRefMATH

Abdul J (1999) Introduction to integral equations with applications. Wiley, New YorkMATH

Khan Y, Va´zquez-Leal H, Wu Q (2013) An efficient iterated method for mathematical biology model. Neural Comput Appl 23:677–682CrossRef

Dehghan M, Shakeri F (2008) Solution of an integro-differential equation arising in oscillating magnetic fields using He’s homotopy perturbation method. Progr Electromag Res 78:361–376CrossRef

Khan Y, Taghipour R, Falahian M, Nikkar A (2013) A new approach to modified regularized long wave equation. Neural Comput Appl 23:1335–1341CrossRef

Elmer CE, Van Vleck ES (2002) A variant of Newton’s method for solution of traveling wave solutions of bistable differential-difference equation. J Dyn Differ Equ 14:493–517CrossRefMATH

10.

Elmer CE, van Vleck ES (2001) Travelling wave solutions for bistable differential-difference equations with periodic diffusion. SIAM J Appl Math 61:1648–1679MathSciNetCrossRefMATH

11.

Khan Y (2013) A method for solving nonlinear time dependent drainage model. Neural Comput Appl 23:411–415CrossRef

12.

Babolian E, Biazar J (2002) Solving the problem of biological species living together by Adomian decomposition method. Appl Math Comput 129:339–343MathSciNetMATH

13.

Shakeri F, Dehghan M (2008) Solution of a model describing biological species living together using the variational iteration method. Math Comput Model 48:685–699MathSciNetCrossRefMATH

14.

Yousefi SA (2011) Numerical solution of a model describing biological species living together by using Legendre multiwavelet method. Int J Non Sci 11(1):109–113MathSciNetMATH

15.

Shakourifar M, Dehghan M (2008) On the numerical solution of nonlinear systems of Volterra integro-differential equations with delay arguments. Computing 82:241–260MathSciNetCrossRefMATH

16.

Adomian G (1990) A review of the decomposition method and some recent results for nonlinear equations. Math Comput Model 13(7):17–43MathSciNetCrossRefMATH

17.

Batiha B, Noorani MSM, Hashim I (2007) Variational iteration method for solving multispecies LotkaVolterra equations. Comput Math Appl 54:903–909MathSciNetCrossRefMATH

18.

Parand K, Razzaghi M (2004) Rational Chebyshev tau method for solving Volterra’s population model. Appl Math Comput 149:893–900MathSciNetMATH

19.

Yüzbaşı Ş (2012) Bessel collocation approach for solving continuous population models for single and interacting species. Appl Math Model 36(8):3787–3802MathSciNetCrossRefMATH

20.

Sedaghat S, Ordokhani Y, Dehghan M (2014) On spectral method for Volterra functional integro-differential equations of neutral type. Numer Funct Anal Optim 35:223–239MathSciNetCrossRefMATH

21.

Yüzbaşı Ş (2012) A numerical approach to solve the model for HIV infection of CD4+T cells. Appl Math Model 36(12):5876–5890MathSciNetCrossRef

22.

Pamuk S (2005) The decomposition method for continuous population models for single and interacting species. Appl Math Comput 163:79–88MathSciNetMATH

23.

Dehghan M, Salehi R (2010) Solution of a nonlinear time-delay model in biology via semi-analytical approaches. Comput Phys Commun 181:1255–1265MathSciNetCrossRefMATH

24.

Pamuk S, Pamuk N (2010) He’s homotopy perturbation method for continuous population models for single and interacting species. Comput Math Appl 59:612–621MathSciNetCrossRefMATH

25.

Yüzbaşı Ş (2011) A numerical approach for solving a class of the nonlinear Lane-Emden type equations arising in astrophysics. Math Method Appl Sci 34(18):2218–2230MathSciNetMATH

26.

Dehghan M, Shakeri F (2010) Solution of parabolic integro-differential equations arising in heat conduction in materials with memory via He’s variational iteration technique. Int J Numer Method Biomed Eng 26:705–715MathSciNetMATH

27.

Merdan M (2007) Homotopy perturbation method for solving a model for HIV infection of CD4+T cells, Istanb. Commer Univ J Sci 12:39–52

28.

Shakeri F, Dehghan M (2011) The finite volume spectral element method to solve turing models in the biological pattern formation. Comput Math Appl 62:4322–4336MathSciNetCrossRefMATH

29.

Yüzbaşı Ş (2013) A numerical approximation for Volterra’s population growth model with fractional order. Appl Math Model 37(5):3216–3227MathSciNetCrossRef

30.

Khan Y, Vázquez-Leal H, Faraz N (2013) An auxiliary parameter method using Adomian polynomials and Laplace transformation for nonlinear differential equations. Appl Math Model 37:2702–2708MathSciNetCrossRef

31.

Khan Y (2014) A novel Laplace decomposition method for non-linear stretching sheet problem in the presence of MHD and slip condition. Int J Numer Methods Heat Fluid Flow 24:73–85MathSciNetCrossRef

32.

Akyüz-Daşcıoğlu A, Sezer M (2005) Chebyshev polynomial solutions of systems of higher-order linear Fredholm-Volterra integro-differential equations. J Franklin Inst 342:688–701MathSciNetCrossRefMATH

33.

Yüzbaşı Ş, Şahin N, Sezer M (2011) Numerical solutions of systems of linear Fredholm integro-differential equations with Bessel polynomial bases. Comput Math Appl 61(10):3079–3096MathSciNetCrossRefMATH

34.

Khan Y, Sayevand K, Fardi M, Ghasemi M (2014) A novel computing multi-parametric homotopy approach for system of linear and nonlinear Fredholm integral equation. Appl Math Comput 249:229–236MathSciNet

35.

Yüzbaşı Ş, Sezer M (2013) An exponential matrix method for solving systems of linear differential equations. Math Method Appl Sci 36(3):336–348MathSciNetCrossRefMATH

36.

Alharbi F (2010) Predefined exponential basis set for half-bounded multi domain spectral method. Appl Math 1:146–152CrossRef

37.

Alipour MM, Domairry G, Davodi AG (2011) An application of exp-function method to approximate general and explicit solutions for nonlinear Schrodinger equations. Numer Method Part Differ Eqs 27:1016–1025MathSciNetCrossRefMATH

38.

Shanmugam R (1998) Generalized exponential and logarithmic polynomials with statistical applications. Int J Math Educ Sci Technol 19(5):659–669MathSciNetCrossRefMATH

39.

Xu M, Chen L, Zeng Z, Li ZB (2010) Reachability analysis of rational eigenvalue linear systems. Int J Syst Sci 41(12):1411–1419MathSciNetCrossRefMATH

40.

Ouerdiane H, Ounaies M (2012) Expansion in series of exponential polynomials of mean-priodic functions. Complex Var Elliptic Eqs 57(5):469–487MathSciNetCrossRefMATH

41.

Debrecen LS (2000) On the extension of exponential polynomials. Math Bohem 125(3):365–370MathSciNet

42.

Ross K (1963) Abstract harmonic analysis I, II. Springer, Berlin

Title: An exponential approach for the system of nonlinear delay integro-differential equations describing biological species living together
Authors: Şuayip Yüzbaşı
Mehmet Sezer
Publication date: 01-04-2016
Publisher: Springer London
Published in: Neural Computing and Applications / Issue 3/2016
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-015-1895-y

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Other articles of this Issue 3/2016

Transferred IR pedestrian detector toward distinct scenarios adaptation

A novel integral extension LMD method based on integral local waveform matching

TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment

Development of a novel flyrock distance prediction model using BPNN for providing blasting operation safety

Classification of electromyography signals using relevance vector machines and fractal dimension

Using neural networks to integrate structural analysis package and optimization package

Premium Partner