Homotopy Methods to Evaluate Linear And Non Linear Partial Differential Equations

Abstract

We focus on linear and nonlinear partial differential equations and we propose the evaluation scheme using Homotopy Perturbation Method (HPM), New Homotopy Perturbation Method (NHPM) and Rational Homotopy Perturbation Method (RHPM) to obtain analytical approximate solutions to them. newlineTo facilitate the benefits of this proposal, an algorithmic form of the HOMOTOPY is also designed to handle the same. In order to illustrate the potentiality of the approach, test problems are offered, and the obtained numerical results are compared with the existing exact solutions and are depicted in terms of plots to reveal its precision and reliability. newline The Homotopy methods will be dedicated towards the exploration of partial and ordinary differential equations of different kinds and their evolution will be discussed. We will also find numerical solution of Linear and nonlinear homogeneous and non-homogeneous differential equations with initial problems which are useful for theory of explosion, exploding wire phenomena, Tsunami, earth quake, astrophysics (explosion in stars), atmosphere of earth and in several other branches of engineering and science. newline newline