Numerical solution of two-dimensional non-linear partial differential equations using hybrid methods

Abstract

This paper is concerned with the numerical solution of two- dimensional non-linear partial
differential equations using a hybrid method. The solution technique involves discritizing the
non-linear system of partial differential equations (PDEs) to obtain a corresponding nonlinear
system of algebraic difference equations to be solved at each time level. To linearize
the resulting system of difference equations, Newton Ralphson root finding algorithm is
applied at each time level with a discrete-node-update scheme. Numerical experiments are
computationally more efficient than the existing methods such as Srivastava et al and Duffy,
D.J.