On modified accelerated monotone iterates for solving semilinear parabolic problems

This paper deals with numerical solutions of nonlinear parabolic problems. Monotone sequences, based on a modified accelerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates a nonlinear parabolic problem. The monotone convergence leads to the existence–uniqueness theorem. An analysis of a convergence rate of the modified accelerated monotone iterative method is given. Numerical experiments are presented.