Stability and convergence of difference scheme for nonlinear evolutionary type equations

Abstract

A finite difference scheme is derived for the initial-boundary problem for the nonlinear equation systemwhere A is a complex diagonal matrix, f is a complex vector function. The stability and convergence in discrete L ∞ -norm of proposed Crank-Nicolson type finite difference schemes is proved. No restrictions on the ratio of time and space grid steps are assumed. Some numerical experiments have been conducted in order to validate the theoretical results.