Application of the Adomian decomposition method for two-dimensional parabolic equation subject to nonstandard boundary specifications

Applied Mathematics and Computation

Volumn 157, Issue 2, 2004, Pages 549-560

  Dehghan, Mehdi ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Adomian decomposition method; Analytic solutions; Boundary element techniques; Closed form solutions; Finite difference schemes; Method of lines; Nonlocal boundary conditions; Parallel algorithms; Specification of energy; Two dimensional parabolic equation

Indexed keywords

ADOMAIN DECOMPOSITION METHOD; ANALYTIC SOLUTIONS; BOUNDARY ELEMENT TECHNIQUES; CLOSED FORM SOLUTIONS; FINITE DIFFERENCE SCHEMES; METHOD OF LINES; NONLOCAL BOUNDARY CONDITIONS; SPECIFICATION OF ENERGY; TWO-DIMENSIONAL PARABOLIC EQUATION;

COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; PARALLEL ALGORITHMS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; SPECTRUM ANALYSIS;

BOUNDARY CONDITIONS;

EID: 4444222587     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.08.098     Document Type: Article

References (32)

1. Adomian G. Solving frontier problems of physics: The decomposition method. 1994;Kluwer, Boston, MA.
2. Adomian G. A review of the decomposition method in applied mathematics. J. Math. Anal. Appl. 135:1988;501-544.
3. Adomian G. Modification of the decomposition approach to the heat equation. J. Math. Anal. Appl. 124:1987;290-291.
4. Adomian G. A new approach to the heat equation,an application of the decomposition method. J. Math. Anal. Appl. 113:1986;202-209.
5. Adomian G. Solving frontier problems modelled by nonlinear partial differential equations. Comput. Math. Appl. 22:1991;91-94.
6. Ang W.T. A method of solution for the one-dimensional heat equation subject to a nonlocal condition. SEA Bull. Math. 26(2):2002;197-203.
7. Cannon J.R., van der Hoek J. Diffusion subject to specification of mass. J. Math. Anal. Appl. 115:1986;517-529.
8. Cannon J.R., Lin Y., Wang S. An implicit finite difference scheme for the diffusion equation subject to mass specification. Int. J. Eng. Sci. 28(7):1990;573-578.
9. Cannon J.R., Esteva S.P., van der Hoek J. A Galerkin procedure for the diffusion equation subject to the specification of mass. SIAM, J. Numer. Anal. 24:1987;499-515.
10. Cannon J.R., Yin H.M. On a class of non-classical parabolic problems. J. Differential Equations. 79:1989;266-288.
11. Capasso V., Kunisch K. A reaction-diffusion system arising in modeling man-environment diseases. Quart. Appl. Math. 46:1988;431-449.
12. Cherruault Y. Convergence of Adomian's method. Math. Comput. Modell. 14:1990;83-86.
13. Datta B.K. A new approach to the wave equation - An application of the decomposition method. J. Math. Anal. Appl. 142:1989;6-12.
14. Day W.A. Existence of a property of solutions of the heat equation subject to linear thermoelasticity and other theories. Quart. Appl. Math. 40:1982;319-330.
15. Day W.A. A decreasing property of solutions of a parabolic equation with applications to thermoelasticity and other theories. Quart. Appl. Math. 41:1983;468-475.
16. Dehghan M. Numerical solution of a parabolic equation with non-local boundary specifications. Appl. Math. Comput. 145:2003;185-194.
17. Dehghan M. Saulyev's techniques for solving a parabolic equation with a non linear boundary specification. Int. J. Comput. Math. 80(2):2003;257-265.
18. Ekolin G. Finite difference methods for a non-local boundary value problem for the heat equation. BIT. 31(2):1991;245-255.
19. Friedman A. Monotonic decay of solutions of parabolic equation with nonlocal boundary conditions. Quart. Appl. Math. 44:1986;468-475.
20. Kawohl B. Remark on a paper by D.A. Day on a maximum principle under nonlocal boundary conditions. Quart. Appl. Math. 45:1987;751-752.
21. Kaya D. An application of the decomposition method to the second-order wave equation. Int. J. Comput. Math. 75:2000;235-245.
22. Lesnic D. A computational algebraic investigation of the decomposition method for time-dependent problems. Appl. Math. Comput. 119:2001;197-206.
23. Lin Y., Xu S., Yin H.M. Finite difference approximations for a class of nonlocal parabolic equations. Int. J. Math. Math. Sci. 20(1):1997;147-164.
24. Y. Lin, Parabolic partial differential equations subject to non-local boundary conditions, Ph.D. dissertation, Department of Pure and Applied Mathematics, Washington State University, 1988.
25. Liu Y. Numerical solution of the heat equation with nonlocal boundary conditions. J. Comput. Appl. Math. 110(1):1999;115-127.
26. Murthy A.S.V., Verwer J.G. Solving parabolic integro-differential equations by an explicit integration method. J. Comput. Appl. Math. 39:1992;121-132.
27. Wang S., Lin Y. A numerical method for the diffusion equation with nonlocal boundary specifications. Int. J. Eng. Sci. 28:1990;543-546.
28. Gumel A.B. On the numerical solution of the diffusion equation subject to the specification of mass. J. Aust. Math. Soc. Ser. B. 40:1999;475-483.
29. Wazwaz A.M. A reliable modification of Adomian decomposition method. Appl. Math. Comput. 102:1999;77-86.
30. Yee E. Application of the decomposition method to the solution of the reaction-convection-diffusion equation. Appl. Math. Comput. 56:1993;1-27.
31. Dehghan M. Locally explicit schemes for three-dimensional diffusion with a non-local boundary condition. Appl. Math. Comput. 138:2003;489-501.
32. Dehghan M. Numerical solution of a non-local boundary value problem with Neumann's boundary conditions. Communications in Numerical Methods in Engineering. 19:2003;1-12.