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Zbl 1157.65515
Chen, Yong; An, Hongli
Homotopy perturbation method for a type of nonlinear coupled equations with parameters derivative. (English)
[J] Appl. Math. Comput. 204, No. 2, 764-772 (2008). ISSN 0096-3003

Summary: The homotopy perturbation method is directly extended to investigate nonlinear coupled equations with parameters derivative and to derive their numerical solutions. These nonlinear coupled equations with parameters derivative contain many important equations of mathematical physics and reaction-diffusion equations. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained. The efficiency and accuracy of the method are verified by using two famous examples: the coupled Burgers and modified Korteweg-de Vries equations. Numerical solutions show that good results have been achieved.

MSC 2000:: *65R20 Integral equations (numerical methods)
45K05 Integro-partial differential equations
35Q53 KdV-like equations

Keywords: homotopy perturbation method; nonlinear coupled systems; fractional derivations; Burgers' equation; numerical examples; rapidly convergent series solution; modified Korteweg-de Vries equations; parameters derivative

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