Difference Method for Solving the Dirichlet Problem for a Multidimensional Integro-Differential Equation of Convection-Diffusion

Abstract

The work is devoted to a numerical method for solving the Dirichlet problem for a multidimensional integro-differential convection-diffusion equation with variable coefficients. Using the method of energy inequalities for solving the first initial-boundary value problem, a priori estimates are obtained in differential and difference interpretations. The obtained estimates imply the uniqueness and stability of the solution of the original differential problem with respect to the right-hand side and initial data, as well as the convergence of the solution of the difference problem to the solution of the original differential problem at a rate of O(| h| + τ). For an approximate solution of the differential problem, an algorithm for the numerical solution was constructed, and numerical calculations of test examples were carried out, illustrating the theoretical calculations obtained.