Numerical solving nonlinear integro-parabolic equations by the monotone weighted average method

The paper deals with numerical solving nonlinear integro-parabolic problems of Volterra type based on the weighted average method. A monotone iterative method is presented. Construction of initial upper and lower solutions is given. 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. Numerical experiments are presented.