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Solving heat and wave-like equations using He’s polynomials. (English) Zbl 1181.80014
Summary: We use He’s polynomials which are calculated form homotopy perturbation method (HPM) for solving heat and wave-like equations. The proposed iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that suggested technique solves nonlinear problems without using Adomian’s polynomials is a clear advantage of this algorithm over the decomposition method.

MSC:
80M25 Other numerical methods (thermodynamics) (MSC2010)
78M25 Numerical methods in optics (MSC2010)
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35A25 Other special methods applied to PDEs
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References:
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