Homotopy perturbation method using laplace transform for ODEs and PDEs

Abstract

The main objective of this thesis entitled Homotopy Perturbation Method Using Laplace Transform for ODEs and PDEs is to study about various types of ordinary and partial diand#64256;erential equations (linear and nonlinear) with their applications in science and engineering arising from chemical sciences, biological sciences, medical sciences, mechanical engineering, electrical engineering, astrophysics, and#64258;uid dynamics, and#64258;uid mechanics etc. For solving such types of problems a numerical technique called homotopy perturbation method using Laplace transform is used. The method is combined with He s polynomial and Laplace transform. newlineIn chapter 1, we describe the basics of homotopy theory and perturbation theory, historical background of LT-HPM; various types of numerical techniques to solve diand#64256;erential equations, which are applicable in the all chapters. newlineIn chapter 2, the Literature review of homotopy perturbation method using Laplace transform (LT-HPM) has been discussed by some authors with their applications. newlineLaplace transform is used for solving Lane-Emden type of diand#64256;erential equations (LETDEs). Also, the method is applicable for solving some numerical examples of LETDEs (homogeneous and nonhomogeneous) of both linear and nonlinear cases. The approximate solutions of these examples are calculated in the form of power series and results obtained after calculating these solutions are compared with those obtained by Adomian decomposition method (ADM). newlineIn chapter 4, delay diand#64256;erential equations and types of delay diand#64256;erential equations (nonlinear and linear, pantograph and multipantograph delay diand#64256;erential equations, respectively) are given with their short introduction. Some numerical examples are included by approximate solutions. The convergence analyses of these diand#64256;erential equations are described by using Banach and#64257;xed point theorem. newlineIn chapter 5, a model is described for determining the temperature in the heterogeneous casting-mould system. This model is occurred in the form of homotopy perturbation method using Laplace