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An Optimal Choice Of Initial Solutions In The Homotopy Perturbation Method, Habibolla Latifizadeh

H. L. Zadeh

This paper proposes a reliable modification of the homotopy perturbation method which can serve as a promising tool for solving a large class of differential equations. In this approach only the highest order derivative is considered in the solution procedure, and the initial solution which can be obtained by the standard procedure is decomposed to optimally match the solution procedure. Some examples are given, showing that only one or few iterations lead to exact solutions using the new technology, while the standard HPM algorithm yields infinite series converging to the exact solutions.