Monotone iterates for solving nonlinear integro-parabolic equations of Volterra type

The paper deals with numerical solving of nonlinear integro-parabolic problems 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.