Homotopy Perturbation Method And Progressive Method Of Consistency, As Well As Related Applications

The computation of highly oscillatory integral integral is a quite important question, so far, there are several methods to solve the highly oscillatory integral. This article mainly say: the first respective narration of the asymptotic method and the homotopy perturbation method; the second obtaining an important result carried on the comparison to the asymptotic method and the homotopy perturbation method; finally giving the concrete numerical example explanation by the homotopy perturbation method in application of the highly oscillatory integral. The asymptotic method is one method solving the highly oscillatory integral and making the error analysis the method. The homotopy perturbation method is the method that combines with the homotopy technology and the perturbation technology. Solving the highly oscillatory integral with application of the homotopy perturbation method is a new application.This paper is composed of five chapters.The first chapter we summarize the highly oscillatory function numerical integration classical method and the most recent development.The second chapter we introduce the asymptotic method asks the univariate highly oscillatory integral as well as in the high degree promotion.The third chapter we introduct the homotopy mapping, perturbation method, as well as the homotopy perturbation method algorithm.The fourth chapter we prove the equivalence of the asymptotic method and the homotopy perturbation method for solving the highly oscillatory integral as well as concrete application.The fifth chapter we give summary and forecast.