The Method of Fractional Steps for the Numerical Solution of a Multidimensional Heat Conduction Equation with Delay for the Case of Variable Coefficient of Heat Conductivity

Abstract

Multidimensional parabolic equations with delay effects in the time component for the case of variable coefficient of heat conductivity depending on spatial and temporal variables are considered. The method of fractional steps is constructed for the numerical solution of these equations. The order of approximation error for the constructed method, stability, and order of convergence are investigated. A theorem is obtained on the order of convergence of the method of fractional steps, which uses the methods from the general theory of difference schemes and the technique of the investigation of difference schemes for solving functional differential equations. Results of calculating test example with variable concentrated and distributed time delay are presented.