Numerical solutions of nonlinear evolution equations using variational iteration method

Authors:
A. A. Soliman;M. A. Abdou
Affiliations:
Department of Mathematics, Faculty of Education (AL-Arish), Suez Canal University, AL-Arish 45111, Egypt;Theoretical Research Group, Department of Physics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

The variational iteration method is used to solve three kinds of nonlinear partial differential equations, coupled nonlinear reaction diffusion equations, Hirota-Satsuma coupled KdV 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. He's variational iteration method is introduced to overcome the difficulty arising in calculating Adomian polynomial in Adomian method. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.