Solving heat and wave-like equations using He’s polynomials.

*(English)*Zbl 1181.80014Summary: 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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\textit{S. T. Mohyud-Din}, Math. Probl. Eng. 2009, Article ID 427516, 12 p. (2009; Zbl 1181.80014)

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##### References:

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