Numerical methods for systems of nonlinear integro-parabolic equations of Volterra type

Abstract

This paper deals with the numerical solution of systems of nonlinear integro-parabolic problems of Volterra type. The numerical approach is based on the method of upper and lower solutions. A monotone iterative method is constructed. Existence and uniqueness of a solution to the nonlinear difference scheme are established. An analysis of convergence rates of the monotone iterative method is given. Construction of initial upper and lower solutions is discussed. Numerical experiments are presented.