A uniform monotone alternating direction scheme for nonlinear singularly perturbed parabolic problems

This paper deals with a monotone alternating direction (ADI) scheme for solving nonlinear singularly perturbed parabolic problems. Monotone sequences, based on the method of upper and lower solutions, are constructed for a nonlinear difference scheme which approximates the nonlinear parabolic problem. The monotone sequences possess quadratic convergence rate. An analysis of uniform convergence of the monotone ADI scheme to the solutions of the nonlinear difference scheme and to the continuous problem is given. Numerical experiments are presented.