A new approach for the application of Adomian decomposition method for the solution of fractional space diffusion equation with insulated ends

Applied Mathematics and Computation

Volumn 202, Issue 2, 2008, Pages 544-549

  Ray, Santanu Saha ^a  

^a HERITAGE INSTITUTE OF TECHNOLOGY   (India)

Author keywords

Adomian decomposition method; Fourier cosine series; Fractional order diffusion equation; Generalized cosine function; Riemann Liouville fractional derivative

Indexed keywords

ADOMIAN DECOMPOSITION METHOD (ADM); DIFFUSION EQUATIONS; FINITE DOMAINS; FRACTIONAL DIFFUSION EQUATION (FDE); NEW APPROACHES;

EID: 48349141442     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.02.043     Document Type: Article

References (40)

1. Mainardi F. Fractional calculus: some basic problems in continuum and statistical mechanics. In: Carpinteri A., and Mainardi F. (Eds). Fractals and Fractional Calculus in Continuum Mechanics (1997), Springer-Verlag, Wien, New York 291-348
2. Mainardi F., Luchko Y., and Pagnini G. The fundamental solution of the space-time fractional diffusion equation. Fractional Calculus and Applied Analysis 4 2 (2001) 153-192
3. Mainardi F., and Pagnini G. The weight functions as solutions of the time-fractional diffusion equation. Applied Mathematics and Computation 141 (2003) 51-62
4. Agrawal O.P. Solution for a fractional diffusion-wave equation defined in a bounded domain. Nonlinear Dynamics 29 (2002) 145-155
5. Metzler R., Barkai E., and Klafter J. Anomalous diffusion and relaxation close to thermal equilibrium: a fractional Fokker-Planck equation approach. Physical Review Letters 82 18 (1999) 3563-3567
6. Metzler R., and Klafter J. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Physics Reports 339 (2000) 1-77
7. Schneider W.R., and Wyss W. Fractional diffusion and wave equations. Journal of Mathematical Physics 30 (1989) 134-144
8. Shen S., and Liu F. Error analysis of an explicit finite difference approximation for the space fractional diffusion equation with insulated ends. ANZIAM Journal 46 E (2005) C871-C887
9. Podlubny I. Fractional Differential Equations (1999), Academic Press, San Diego, California, USA
10. Adomian G. Nonlinear Stochastic Systems theory and Applications to Physics (1989), Kluwer Academic Publishers, Netherlands
11. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer Academic Publishers, Boston
12. Adomian G. An Analytical solution of the stochastic Navier-Stokes system. Foundations of Physics 21 7 (1991) 831-843
13. Adomian G., and Rach R. Linear and nonlinear Schrödinger equations. Foundations of Physics 21 (1991) 983-991
14. Adomian G. Solution of physical problems by decomposition. Computers and Mathematics with Applications 27 9/10 (1994) 145-154
15. Adomian G. Solutions of nonlinear partial differential equations. Applied Mathematics Letters 11 3 (1998) 121-123
16. Abbaoui K., and Cherruault Y. The decomposition method applied to the cauchy problem. Kybernetes 28 (1999) 103-108
17. Kaya D., and Yokus A. A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations. Mathematics and Computers in Simulation 60 6 (2002) 507-512
18. Wazwaz A. A reliable modification of adomian decomposition method. Applied Mathematics and Computation 102 1 (1999) 77-86
19. Kaya D., and El-Sayed S.M. On a generalized fifth order KdV equations. Physics Letters A 310 1 (2003) 44-51
20. Kaya D., and El-Sayed S.M. An application of the decomposition method for the generalized KdV and RLW equations. Chaos, Solitons and Fractals 17 5 (2003) 869-877
21. Kaya D. An explicit and numerical solutions of some fifth-order KdV equation by decomposition method. Applied Mathematics and Computation 144 2-3 (2003) 353-363
22. Kaya D. A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation. Applied Mathematics and Computation 149 3 (2004) 833-841
23. Kaya D. Solitary wave solutions for a generalized Hirota-Satsuma coupled Kdv equation. Applied Mathematics and Computation 147 1 (2004) 69-78
24. Kaya D., and Inan I.E. A numerical application of the decomposition method for the combined KdV-MKdV equation. Applied Mathematics and Computation 168 2 (2005) 915-926
25. El-Sayed S.M., and Kaya D. A numerical solution and an exact explicit solution of the NLS equation. Applied Mathematics and Computation 172 2 (2006) 1315-1322
26. Kaya D. The exact and numerical solitary-wave solutions for generalized modified Boussinesq equation. Physics Letters A 348 3-6 (2006) 244-250
27. Shawagfeh N.T. The decompostion method for fractional differential equations. Journal of Fractional Calculus 16 (1999) 27-33
28. Shawagfeh N.T. Analytical approximate solutions for nonlinear fractional differential equations. Applied Mathematics and Computation 131 (2002) 517-529
29. Saha Ray S., and Bera R.K. Solution of an extraordinary differential equation by adomian decomposition method. Journal of Applied Mathematics 4 (2004) 331-338
30. Saha Ray S., and Bera R.K. Analytical solution of a dynamic system containing fractional derivative of order one-half by Adomian decomposition method. Transaction ASME Journal of Applied Mechanics 72 2 (2005) 290-295
31. Saha Ray S., and Bera R.K. An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method. Applied Mathematics and Computation 167 1 (2005) 561-571
32. Saha Ray S., and Bera R.K. Analytical solution of the Bagley Torvik equation by Adomian decomposition method. Applied Mathematics and Computation 168 1 (2005) 398-410
33. Saha Ray S., Chaudhuri K.S., and Bera R.K. Analytical approximate solution of nonlinear dynamic system containing fractional derivative by modified decomposition method. Applied Mathematics and Computation 182 1 (2006) 544-552
34. Saha Ray S. Exact solutions for time-fractional diffusion-wave equations by decomposition method. Physica Scripta 75 (2007) 53-61
35. Samko S., Kilbas A., and Marichev O. Fractional Integrals and Derivatives: Theory and Applications (1993), Gordon and Breach, London
36. Cherruault Y. Convergence of Adomian's method. Kybernetes 18 (1989) 31-38
37. Abbaoui K., and Cherruault Y. Convergence of Adomian's method applied to differential equations. Computers and Mathematics with Applications 28 5 (1994) 103-109
38. Abbaoui K., and Cherruault Y. New ideas for proving convergence of decomposition methods. Computers and Mathematics with Applications 29 (1995) 103-108
39. Himoun N., Abbaoui K., and Cherruault Y. New results of convergence of Adomian's method. Kybernetes 28 4-5 (1999) 423-429
40. Wolfram S. Mathematica for Windows, Version 5.0 (2003), Wolfram Research