Modeling convection–diffusion processes based on a multidimensional integro-differential equation with degenerate parabolicity

An initial–boundary-value problem for a multidimensional integro-differential equation with degenerate parabolicity is considered. Based on the maximum-principle theorem and splitting method, a nonlinear monotonic high-order (higher than the first) numerical scheme is constructed for an implicit two-layer scheme. For the error of a numerical solution, a priori estimates are obtained and the sufficient convergence conditions are proved. A posteriori estimates for the numerical error of the solution are analyzed. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 83–96, March–April 2009.