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Convergence of the homotopy perturbation method for partial differential equations. (English) Zbl 1173.35395
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:
35C05 Solutions to PDEs in closed form
35K25 Higher-order parabolic equations
35K55 Nonlinear parabolic equations
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