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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:
80M25Other numerical methods (thermodynamics)
78M25Numerical methods in optics
65L15Eigenvalue problems for ODE (numerical methods)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
35A25Other special methods (PDE)