The variational iteration method for solving linear and nonlinear systems of PDEs

Computers and Mathematics with Applications

Volumn 54, Issue 7-8, 2007, Pages 895-902

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Systems of PDEs; Variational iteration method

Indexed keywords

ITERATIVE METHODS; NONLINEAR ANALYSIS; NONLINEAR SYSTEMS; NUMERICAL METHODS; VARIATIONAL TECHNIQUES;

ANALYTIC TREATMENT; CALCULATION SIZE; NONLINEAR TERMS; VARIATIONAL ITERATION METHOD (VIM);

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 34748859114     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.12.059     Document Type: Article

References (24)

1. He J.H. Some asymptotic methods for strongly nonlinear equations. Int. J. Modern Phys. B 20 10 (2006) 1141-1199
2. J.H. He, Non-perturbative methods for strongly nonlinear problems, Dissertation.de-Verlag im Internet GmbH, Berlin, 2006
3. He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Methods Appl. Mech. Engrg. 167 (1998) 57-68
4. He J.H. Variational iteration method for autonomous ordinary differential systems. Appl. Math. Comput. 114 2/3 (2000) 115-123
5. He J.H., and Wu X.H. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos Solitons Fractals 29 1 (2006) 108-113
6. He J.H. A new approach to nonlinear partial differential equations. Commun. Nonlinear Sci. Numer. Simul. 2 4 (1997) 203-205
7. He J.H. A variational iteration approach to nonlinear problems and its applications. Mech. Appl. 20 1 (1998) 30-31 (in Chinese)
8. He J.H. Variational iteration method-a kind of nonlinear analytical technique: Some examples. Int. J. Nonlinear Mech. 34 (1999) 699-708
9. He J.H. A generalized variational principle in micromorphic thermoelasticity. Mech. Res. Commun. 32 (2005) 93-98
10. J.H. He, Variational iteration method-some recent results and new interpretations, J. Comput. Appl. Math. (2006) (in press)
11. Abulwafa E.M., Abdou M.A., and Mahmoud A.A. The solution of nonlinear coagulation problem with mass loss. Chaos Solitons Fractals 29 (2006) 313-330
12. Momani S., and Odibat Z. Analytical approach to linear fractional partial differential equations arising in fluid mechanics. Phys. Lett. A 1 53 (2006) 1-9
13. Momani S., and Abusaad S. Application of He's variational-iteration method to Helmholtz equation. Chaos Solitons Fractals 27 5 (2005) 1119-1123
14. Abdou M.A., and Soliman A.A. Variational iteration method for solving Burgers' and coupled Burgers' equation. J. Comput. Appl. Math. 181 (2005) 245-251
15. A.M. Wazwaz, A comparison between the variational iteration method and Adomian decomposition method, J. Comput. Appl. Math. (2006) (in press)
16. A.M. Wazwaz, The variational iteration method for rational solutions for KdV, K(2,2), Burgers, and cubic Boussinesq equations, J. Comput. Appl. Math. (2006) (in press)
17. Wazwaz A.M. Partial Differential Equations: Methods and Applications (2002), Balkema Publishers, The Netherlands
18. Wazwaz A.M. Necessary conditions for the appearance of noise terms in decomposition solution series. Appl. Math. Comput. 81 (1997) 265-274
19. Wazwaz A.M. A new technique for calculating Adomian polynomials for nonlinear polynomials. Appl. Math. Comput. 111 1 (2000) 33-51
20. Wazwaz A.M. A new method for solving singular initial value problems in the second order differential equations. Appl. Math. Comput. 128 (2002) 47-57
21. Wazwaz A.M. A First Course in Integral Equations (1997), World Scientific, Singapore
22. Wazwaz A.M. Analytical approximations and Padé approximants for Volterra's population model. Appl. Math. Comput. 100 (1999) 13-25
23. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer, Boston
24. Adomian G. A review of the decomposition method in applied mathematics. J. Math. Anal. Appl. 135 (1988) 501-544