Uniform convergent monotone iterates for semilinear singularly perturbed parabolic problems

Abstract

a b s t r a c tThis paper deals with discrete monotone iterative methods for solving semilinear singularly perturbed parabolic problems. Monotone sequences, based on the accelerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem. This monotone convergence leads to the existence-uniqueness theorem. An analysis of uniform convergence of the monotone iterative method to the solutions of the nonlinear difference scheme and continuous problem is given. Numerical experiments are presented.

Iterative analytic approximation to one‐dimensional nonlinear reaction–diffusion equations

“…23,24 However, the convergence is linear. On the other hand, Boglaev 25 extends the idea of the accelerated monotone iterative method originally presented in Pao 26 to nonlinear reaction-diffusion problems. The paper further investigates the convergence properties of the proposed monotone iterative method.…”