The Technique Homotopy Perturbation Method Operated on Laplace Equation

Abstract

In this study, we introduce a technique acknowledged as the Homotopy Perturbation Method (HPM) for obtaining the particular solution of two-dimensional Laplace’s Equation with conditions like Dirichlet, Neumann and the use of different boundary prerequisites to exhibit this method’s potential and reliability. The steady-state condition, which depends on temperature, converts Laplace’s equation into a greater dimension and deforms the equal into a Partial Differential Equation (PDE). Here we additionally tried to discover a comparative measurement in terms of literature survey [1] between the results bought by means of the HPM approach and the same result for the identical equation introduced in any other technique eventually referred to as the Variable Separation Method (VSM). The consequences exhibit that HPM has excessive efficiency and effectiveness in fixing Laplace’s equation.  Also dealing without delay with the trouble has a wide variety of benefits and furnished the approximate solution which converges very unexpectedly to a correct answer.