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Biazar, J.; Ghazvini, H.

Convergence of the homotopy perturbation method for partial differential equations. (English) Zbl 1173.35395

Nonlinear Anal., Real World Appl. 10, No. 5, 2633-2640 (2009).
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.

Cited in 37 Documents

MSC:

35C05 Solutions to PDEs in closed form
35K25 Higher-order parabolic equations
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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\textit{J. Biazar} and \textit{H. Ghazvini}, Nonlinear Anal., Real World Appl. 10, No. 5, 2633--2640 (2009; Zbl 1173.35395)
Full Text: DOI

References:

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