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Homotopy perturbation method for a type of nonlinear coupled equations with parameters derivative. (English) Zbl 1157.65515
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.
65R20Integral equations (numerical methods)
45K05Integro-partial differential equations
35Q53KdV-like (Korteweg-de Vries) equations