“COMPARATIVE NUMERICAL ACCURACY OF COLLOCATION AND FINITE ELEMENT METHODS FOR SOLVING NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS”

Abstract

The objective of this paper is to compare numerical accuracy concerning the convergence rate of numerical techniques - collocation method & finite element method with a focus on Berger’s equation Using the Cubic Hermite Collocation Method (CHCM) and the Least Squares Quadratic B-Spline Finite Element Method (LSQ-FEM), we evaluate their numerical accuracy, convergence rate, and computational efficiency. The Cole–Hopf transformation is employed to obtain the analytical form of the exact solution for validation. Such insights into the strengths and weaknesses of each approach are provided by this study. Also errors are presented with respect to the exact solution along with a graphical illustration.