Numerical Solutions of Nonlinear Parabolic Problems by Monotone Jacobi and Gauss-Seidel Methods

Abstract

This paper is concerned with solving nonlinear monotone difference schemes of the parabolic type. The monotone Jacobi and monotone Gauss-Seidel methods are constructed. Convergence rates of the methods are compared and estimated. The proposed methods are applied to solving nonlinear singularly perturbed parabolic problems. Uniform convergence of the monotone methods is proved. Numerical experiments complement the theoretical results.