A STUDY ON THE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS BY SOME VARIATIONAL ITERATIVE TECHNIQUE

Abstract

Nonlinear partial differential equations (PDEs) arise in a wide range of scientific and engineering applications, including fluid dynamics, solid mechanics, and heat transfer. However, finding exact solutions to nonlinear PDEs is often difficult or impossible. Therefore, there is a need for reliable and efficient numerical methods for solving these equations. One promising approach is the variational iteration method (VIM), which is a semi-analytical method that combines the ideas of variational calculus and iteration methods. The VIM has been successfully applied to solve a variety of nonlinear PDEs, including the Navier-Stokes equations, the Korteweg-de Vries equation, and the Burgers' equation. In this study, we will investigate the application of the VIM to solve two important nonlinear PDEs: the FitzHugh-Nagumo equation and the Lotka-Volterra model. We will show that the VIM can provide accurate and efficient solutions to these equations.