Numerical simulation of equal-width wave equation

Computers and Mathematics with Applications

Volumn 54, Issue 7-8, 2007, Pages 1147-1153

  Yusufoglu, Elcin ^a   Bekir, Ahmet ^a  

^a DUMLUPINAR UNIVERSITY   (Turkey)

Author keywords

Adomian decomposition method; Correction functional; Equal width wave equation; General Lagrange multiplier; Variational iteration method

Indexed keywords

COMPUTER SIMULATION; ERROR CORRECTION; ITERATIVE METHODS; LAGRANGE MULTIPLIERS; NONLINEAR EQUATIONS; NUMERICAL METHODS; VARIATIONAL TECHNIQUES;

ADOMIAN DECOMPOSITION METHOD; CORRECTION FUNCTIONAL; EQUAL WIDTH WAVE EQUATION; VARIATIONAL ITERATION METHOD;

WAVE EQUATIONS;

EID: 34748914168     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.12.080     Document Type: Article

References (24)

1. Ablowitz M.J., and Clarkson P.A. Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform (1990), Cambridge University Press, Cambridge
2. He J.-H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Methods Appl. Mech. Engrg. 167 (1998) 57-68
3. He J.-H. Approximate solution of nonlinear differential equations with convolution product non-linearities. Comput. Methods Appl. Mech. Engrg. 167 (1998) 69-73
4. He J.-H. Variational iteration method-a kind of non-linear analytical technique: Some examples. Internat. J. Non-Linear Mech. 34 (1999) 699-708
5. He J.-H. Variational iteration method for autonomous ordinary differential systems. Appl. Math. Comput. 114 (2000) 115-123
6. He J.-H., and Wu X.-H. Construction of solitary solution and compaction-like solution by variational iteration method. Chaos Soliton Fractals 29 1 (2006) 108-113
7. Draganescu Gh.E., and Capalnasan V. Nonlinear relaxation phenomena in polycrystalline solids. Int. J. Circuit Theory Appl. 4 3 (2003) 219-226
8. He J.-H., Wan Y.Q., and Guo Q. An iteration formulation for normalized diode characteristics. Int. J. Circuit Theory Appl. 32 6 (2004) 629-632
9. Bildik N., and Konuralp A. The use of Variational Iteration Method, Differential Transform Method and Adomian Decomposition Method for solving different types of nonlinear partial differential equations. Int. J. Nonlinear Sci. Numer. Simul. 7 1 (2006) 65-70
10. Odibat Z.M., and Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. Int. J. Nonlinear Sci. Numer. Simul. 7 (2006) 27-34
11. Abdou M.A., and Soliman A.A. Variational iteration method for solving Burger's and coupled Burger's equations. J. Comput. Appl. Math. 181 (2005) 245-251
12. Soliman A.A. A numerical simulation and explicit solutions of KdV-Burger's and Lax's seventh-order KdV equations. Chaos Solitons Fractals 29 (2006) 294-302
13. Abulwafa E.M., Abdou M.A., and Mahmoud A.A. The solution of nonlinear coagulation problem with mass loss. Chaos Solitons Fractals 26 (2006) 313-330
14. He J.-H. Some asymptotic methods for strongly nonlinear equations. Inter. J. Modern Phys. B 20 10 (2006) 1141-1199
15. Adomian G. Solving Frontier Problems of Physics: The Decomposition Methods (1994), Kluwer Academic Publishers, Boston
16. Wazwaz A.M. A reliable modification of Adomian decomposition method. Appl. Math. Comput. 102 (1997) 77-86
17. Wazwaz A.M. A new algorithm for calculating Adomian polynomials for nonlinear operators. Appl. Math. Comput. 111 (2000) 53-69
18. He J.-H. Variational principle for some nonlinear partial differential equations with variable coefficients. Chaos Solitons Fractals 19 4 (2004) 847-851
19. Liu H.M. Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method. Chaos Solitons Fractals 23 2 (2005) 573-576
20. Raslan K.R. Collocation method using quartic B-spline for the equal width (EW) equation. Appl. Math. Comput. 168 (2005) 795-805
21. Dogan A. Application of Galerkin's method to equal width wave equation. Appl. Math. Comput. 160 1 (2005) 65-76
22. Zaki S.I. A least square finite element scheme for the EW equation. Comput. Methods Appl. Mech. Engrg. 189 (2000) 587-594
23. Zaki S.I. Solitary waves induced by the boundary forced EW equation. Comput. Methods Appl. Mech. Engrg. 190 (2001) 4881-4887
24. Cherruault Y., and Adomian G. Decomposition methods: A new proof of convergence. Math. Comput. Modelling 18 12 (1993) 103-106