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He-Laplace method for linear and nonlinear partial differential equations. (English) Zbl 1251.65146

Summary: A new treatment for homotopy perturbation method is introduced. The new treatment is called He-Laplace method which is the coupling of the Laplace transform and the homotopy perturbation method using He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The method is implemented on linear and nonlinear partial differential equations. It is found that the proposed scheme provides the solution without any discretization or restrictive assumptions and avoids the round-off errors.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
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