The Numerical Implementation of the Linear Integro- Differential Equations Method for the Solution of Non-Stationary Heat Conduction Problem with Two Space Variables

摘要

The paper proposes a general method for solution of non-stationary heat conduction problem with two space variables. It is based on Finite Element Method, which uses the operator of the interlineation on a given system of lines. The region of consideration divided on rectangular or triangular elements with curvilinear sides belonging to the boundary of the domain. Interlineation of functions is a restoration of the function with the help of its traces on the system of lines. Operators of interlineations allow to restore functions of two or more variables between the lines using their traces and traces of their partial derivatives up to a given order on the indicated lines. Application of the method on examples of solutions of the nonstationary heat conduction equation for regions of complex shape is illustrated.