The use of the Adomian decomposition method for solving a parabolic equation with temperature overspecification

Physica Scripta

Volumn 73, Issue 3, 2006, Pages 240-245

  Dehghan, Mehdi ^a,b   Tatari, Mehdi ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

^b INSTITUTE FOR STUDIES IN THEORETICAL PHYSICS AND MATHEMATICS IPM   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; APPROXIMATION THEORY; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; THERMAL EFFECTS;

DISCRETIZATION; PARABOLIC PARTIAL DIFFERENTIAL EQUATION; SPATIAL DOMAIN;

PROBLEM SOLVING;

EID: 33745480762     PISSN: 00318949     EISSN: 14024896     Source Type: Journal    
DOI: 10.1088/0031-8949/73/3/002     Document Type: Article

References (31)

1. Cannon J R and Lin Y 1988 Determination of parameter p(t) in Holder classes for some semilinear parabolic equations Inverse Problems 4 595-606
2. Dehghan M 2003 Determination of a control function in three-dimensional parabolic equations Math. Comput. Simul. 61 89-100
3. Dehghan M 2003 Finding a control parameter in one-dimensional parabolic equation Appl. Math. Comput. 135 491-503
4. Cannon J R, Lin Y and Wang S 1992 Determination of source parameter in parabolic equations Meccanica 27 85-94
5. Cannon J R and Yin H M 1991 On a class of nonlinear parabolic equations with nonlinear trace type functionals Inverse Problems 7 149-61
6. Cannon J R and Lin Y 1990 Numerical solutions of some parabolic inverse problems Numer. Meth. Partial Diff. Eqns 2 177-91
7. Cannon J R and Lin Y 1990 An inverse problem of finding a parameter in a semilinear heat equation J. Math. Anal. Appl. 145 470-84
8. Cannon J R and Yin H M 1989 On a class of non-classical parabolic problems J. Diff. Eqns 79 266-88
9. Day W A 1982 Extension of a property of the heat equation to linear thermoelasticity and other theories Q. Appl. Math. 40 319-30
10. Dehghan M 2002 Fourth-order techniques for identifying a control parameter in the parabolic equations Int. J. Eng. Sci. 40 433-47
11. Abbaoui K and Cherruault Y 1995 New ideas for proving convergence of decomposition methods Comput. Math. Appl. 29 103-8
12. Adomian G 1988 A rewiew of the decompositiom method in applied mathematics J. Math. Anal. Appl. 135 501-44
13. Babolian E and Biazar J 2002 On the order of convergence of Adomian method Appl. Math. Comput. 130 383-7
14. Cherruault Y 1990 Convergence of Adomian's decomposition method Math. Comput. Model 14 83-6
15. Cherruault Y, Adomian G, Abbaoui K and Rach R 1995 Further remarks on convergence of decomposition method Int. J. Biomed. Comput. 38 89-93
16. Cherruault Y, Inc M and Abbaoui K 2002 On the solution of the nonlinear Korteweg-de Vries equation by the decomposition method Kybernetes 31 766-72
17. Chrysos M, Sanchez F and Cherruault Y 2002 Improvement of convergence of Adomian's method using Padé approximants Kybernetes 31 884-95
18. Adomian G 1994 Solving Frontier Problems of Physics: The Decomposition Method (Boston, MA: Kluwer)
19. Wazwaz A M 1999 A reliable modification of Adomian decomposition method Appl. Math. Comput. 102 77-86
20. Wazwaz A M and Khuri S 1996 A reliable technique for solving the weakly singular second-kind Volterra-type integral equations Appl. Math. Comput. 80 287-99
21. Wazwaz A M and El-Sayed S M 2001 A new modification of the Adomian decomposition method for linear and nonlinear operators Appl. Math. Comput. 122 393-405
22. Guellal S and Cherruault Y 1995 Application of the decomposition method to identify the distributed parameters of an elliptical equation Math. Comput. Modelling 21 51-5
23. Lesnic D and Elliott L 1999 The Decomposition Approach to inverse heat conduction J. Math. Anal. Appl. 232 82-98
24. Répaci A 1989 Bellman-Adomian solutions of nonlinear inverse problems in continuum physics J. Math. Anal. Appl. 143 57-65
25. Répaci A 1989 On the solution of a class of inverse evolution problems by Bellman-Adomian method Appl. Math. Lett. 2 151-3
26. Dehghan M 2004 The use of Adomian decomposition method for solving the one dimentional parabolic equation with non-local boundary spesification Int. J. Comput. Math. 81 25-34
27. Dehghan M 2004 The solution of a nonclassic problem for one-dimensional hyperbolic equation using the decomposition procedure Int. J. Comput. Math. 81 979-89
28. Tatari M and Dehghan M 2005 Numerical solution of Laplace equation in a disk using the Adomian decomposition method Phys. Scr. 72 345-8
29. Wazwaz A M 2000 A new algorithm for calculating Adomian polynomials for nonlinear operators Appl. Math. Comput. 111 53-69
30. Ngarhasta N, Some B, Abbaoui K and Cherruault Y 2002 New numerical study of Adomian method applied to a diffusion mode Kybernetes 31 61-75
31. Adomian G 1991 Solving frontier problems modeled by nonlinear partial differential equations Comput. Math. Appl. 22 91-4