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Numerical solutions of nonlinear evolution equations using variational iteration method. (English) Zbl 1120.65111

Summary: The variational iteration method is used to solve three kinds of nonlinear partial differential equations, coupled nonlinear reaction diffusion equations, Hirota-Satsuma coupled Korteweg-de Vries system and Drinefel’d-Sokolov-Wilson equations. Numerical solutions obtained by the variational iteration method are compared with the exact solutions, revealing that the obtained solutions are of high accuracy. J. H. He’s variational iteration method [Int. J. Non-Linear Mech. 34, No. 4, 699–708 (1999; Zbl 1342.34005)] is introduced to overcome the difficulty arising in calculating Adomian’s polynomial in Adomian’s method. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
35Q53 KdV equations (Korteweg-de Vries equations)

Citations:

Zbl 1342.34005
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References:

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