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Zbl 1173.35395
Biazar, J.; Ghazvini, H.
Convergence of the homotopy perturbation method for partial differential equations. (English)
[J] Nonlinear Anal., Real World Appl. 10, No. 5, 2633-2640 (2009). ISSN 1468-1218

Summary: We introduce a homotopy perturbation method to obtain exact solutions to some linear and nonlinear partial differential equations. This method is a powerful device for solving a wide variety of problems. Using the homotopy perturbation method, it is possible to find the exact solution or an approximate solution of the problem. Convergence of the method is proved. Some examples such as Burgers', Schrödinger and fourth order parabolic partial differential equations are presented, to verify convergence hypothesis, and illustrating the efficiency and simplicity of the method.

MSC 2000:: *35C05 Solutions of PDE in closed form
35K25 Higher order parabolic equations, general
35K55 Nonlinear parabolic equations

Keywords: homotopy perturbation method; partial differential equations; Burgers' equations; Schrödinger equations; fourth order parabolic equations; convergence sequence

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Zentralblatt MATH Berlin [Germany]