Numerical Simulation of Singularly Perturbed Reaction-Diffusion Equation Using Finite Element Method

This article deals with the study of sign-changing solutions of the nonlinear singularly perturbed reaction-diffusion equation. Sign changing solutions of the nonlinear problem do not appear to have been previously studied in detail computationally, and it is hoped that this paper will help to provide a new idea in this direction. A variant of Newton’s method having tenth order of convergence has been established to linearize the nonlinear system of equations. Examples of the nonlinear problem having nonlinearities in homogeneous/nonhomogeneous form are considered to show the existence of solutions.