Solution of a model describing biological species living together using the variational iteration method

Mathematical and Computer Modelling

Volumn 48, Issue 5-6, 2008, Pages 685-699

  Shakeri, Fatemeh ^a   Dehghan, Mehdi ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Adomian decomposition method; Integro differential equation; Mathematical biology; Pseudospectral Legendre method; The equilibrium state of two species living together; Variational iteration method

Indexed keywords

BESSEL FUNCTIONS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); INTEGRAL EQUATIONS; INTEGRODIFFERENTIAL EQUATIONS; LAGRANGE MULTIPLIERS; NONLINEAR EQUATIONS; OSCILLATORS (MECHANICAL); PARTICLE SIZE ANALYSIS;

ADOMIAN DECOMPOSITION METHOD (ADM); BIOLOGICAL SPECIES; DISCRETIZATION; ELSEVIER (CO); EXACT SOLUTIONS; GENERAL (CO); LAG RANGE; LEGENDRE; NONLINEAR INTEGRO DIFFERENTIAL EQUATIONS; PSEUDOSPECTRAL; SMALL PERTURBATIONS; TEST PROBLEMS; VARIATIONAL ITERATION METHOD (VIM); VARIATIONAL ITERATION TECHNIQUE;

ITERATIVE METHODS;

EID: 47949123722     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2007.11.012     Document Type: Article

References (47)

1. He J.H. Approximate solution of nonlinear differential equations with convolution product nonlinearities. Computer Methods in Applied Mechanics and Engineering 167 (1998) 57-68
2. He J.H. Variational iteration method for autonomous ordinary differential systems. Appl. Math. Comput. 114 (2000) 115-123
3. He J.H. Approximate analytical solution of Blasius' equation. Communications in Nonlinear Science and Numerical Simulation 4 (1999) 75-78
4. Dehghan M., and Tatari M. The use of He's variational iteration method for solving the Fokker-Planck equation. Phys. Scr. 74 (2006) 310-316
5. Abbasbandy S. An approximation solution of a nonlinear equation with Riemann Liouville's fractional derivatives by He's variational iteration method. J. Comput. Appl. Math. 207 (2007) 53-58
6. Słota D. Direct and inverse one-phase Stefan problem solved by the variational iteration method. Comput. Math. Appl. 54 (2007) 1139-1146
7. Sweilam N.H. Harmonic wave generation in non linear thermoelasticity by variational iteration method and Adomian's method. J. Comput. Appl. Math. 207 (2007) 64-72
8. Wazwaz A.M. The variational iteration method for a reliable treatment of the linear and the nonlinear Goursat problem. Appl. Math. Comput. 193 (2007) 455-462
9. Shakeri F., and Dehghan M. Numerical solution of the Klein-Gordon equation via He's variational iteration method. Nonlinear Dyn. 51 (2008) 89-97
10. Tian L., and Yin J. Shock-peakon and shock-compacton solutions for K (p, q) equation by variational iteration method. J. Comput. Appl. Math. 207 (2007) 46-52
11. Batiha B., Noorani M.S.M., and Hashim I. Application of variational iteration method to the generalized Burgers-Huxley equation. Chaos Solitons Fractals 36 (2008) 660-663
12. Tatari M., and Dehghan M. Solution of problems in calculus of variations via He's variational iteration method. Phys. Lett. A 362 (2007) 401-406
13. He J.H., and Wu X.H. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos Solitons Fractals 29 (2006) 108-113
14. Javidi M., and Golbabai A. Exact and numerical solitary wave solutions of generalized Zakharov equation by the variational iteration method. Chaos Solitons Fractals 36 (2008) 309-313
15. Ganji D.D., Jannatabadi M., and Mohseni E. Application of He's variational iteration method to nonlinear Jaulent Miodek equations and comparing it with ADM. J. Comput. Appl. Math. 207 (2007) 35-45
16. M. Dehghan, F. Shakeri, Application of He's variational iteration method for solving the Cauchy reaction-diffusion problem, J. Comput. Appl. Math. (2007) (in press)
17. Lu J. Variational iteration method for solving two-point boundary value problems. J. Comput. Appl. Math. 207 (2007) 92-95
18. Sweilam N.H. Variational iteration method for solving cubic nonlinear Schrodinger equation. J. Comput. Appl. Math. 207 (2007) 155-163
19. L.M.B. Assas, Variational iteration method for solving coupled-KdV equations, Chaos Solitons Fractals (2007) (in press)
20. Batiha B., Noorani M.S.M., and Hashim I. Variational iteration method for solving multispecies Lotka-Volterra equations. Comput. Math. Appl. 54 (2007) 903-909
21. Abulwafa E.M., Abdou M.A., and Mahmoud A.A. Solution of nonlinear coagulation problem with mass loss. Chaos Solitons Fractals 29 (2006) 313-330
22. Odibat Z., and Momani S. Numerical methods for nonlinear partial differential equations of fractional order. Appl. Math. Model. 32 (2008) 28-39
23. Xu L. Variational iteration method for solving integral equations. Comput. Math. Appl. 54 (2007) 1071-1078
24. Sweilam N.H. Fourth order integro-differential equations using variational iteration method. Comput. Math. Appl. 54 (2007) 1086-1091
25. Wazwaz A.M. The variational iteration method for solving two forms of Blasius equation on a half-infinite domain. Appl. Math. Comput. 188 (2007) 485-491
26. Dehghan M., and Tatari M. The use of Adomian decomposition method for solving problems in calculus of variations. Math. Probl. Eng. (2006) 1-12
27. Momoniat E., Selway T.A., and Jina K. Analysis of Adomian decomposition applied to a third-order ordinary differential equation from thin film flow. Nonlinear Analysis: Theory, Methods and Applications 66 (2007) 2315-2324
28. Saha Ray S., and Bera R.K. Analytical solution of a fractional diffusion equation by Adomian decomposition method. Appl. Math. Comput. 174 (2006) 329-336
29. Saha Ray S., and Bera R.K. An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method. Appl. Math. Comput. 167 (2005) 561-571
30. He J.H. Some asymptotic methods for strongly nonlinear equations. Internat. J. Modern Phys. B 20 (2006) 1141-1199
31. Cveticanin L. Homotopy perturbation method for pure nonlinear differential equation. Chaos Solitons Fractals 30 (2006) 1221-1230
32. Dehghan M., and Shakeri F. Solution of an integro-differential equation arising in oscillating magnetic fields using He's homotopy perturbation method. Progr. Electromag. Res. 78 (2008) 361-376
33. Shakeri F., and Dehghan M. Inverse problem of diffusion equation by He's homotopy perturbation method. Phys. Scripta 75 (2007) 551-556
34. Canuto C., Hussaini M.Y., Quarteroni A., and Zhang T.A. Spectral Methods in Fluid Dynamic (1988), Prentice-Hall, Englewood Cliffs, NJ
35. Saadatmandi A., and Dehghan M. Numerical solution of the one-dimensional wave equation with an integral condition. Numer. Methods Partial Differential Equations 23 (2007) 282-292
36. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer Academic
37. Adomian G. A review of the decomposition method in applied mathematics, I. Math. Anal. Appl. 135 (1988) 501-544
38. Babolian E., and Biazar J. Solving the problem of biological species living together by Adomian decomposition method. Appl. Math. Comput. 129 (2002) 339-343
39. A.J. Jerri, Introduction to integral equations with applications, 1999
40. Dehghan M. Efficient techniques for the second-order parabolic equation subject to nonlocal specifications. Appl. Numer. Math. 52 (2005) 39-62
41. Dehghan M. Parameter determination in a partial differential equation from the overspecified data. Math. Comput. Modelling 41 (2005) 196-213
42. Dehghan M. On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation. Numer. Methods Partial Differential Equations 21 1 (2005) 24-40
43. Dehghan M. Implicit collocation technique for heat equation with non-classic initial condition. Int. J. Nonlinear Sci. Numer. Simul. 7 (2006) 447-450
44. Dehghan M. Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices. Math. Comput. Simulation 71 (2006) 16-30
45. Dehghan M. A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications. Numer. Methods Partial Differential Equations 22 (2006) 220-257
46. Dehghan M. Time-splitting procedures for the solution of the two-dimensional transport equation. Kybernetes 36 (2007) 791-805
47. Dehghan M. The one-dimensional heat equation subject to a boundary integral specification. Chaos Solitons Fractals 32 (2007) 661-675