Development the Regularization Computing Method for Solving Boundary Value Problem to Heat Equation in the Composite Materials

Abstract

In this paper, the heat conduction equation for composite materials posed and solved. The inverse Boundary Value Problem (BVP) described and solved. By studying and solving the direct problem for the heat equation in composite materials, we can determine the function spaces and solve the inverse problem. The Sturm-Liouville method was used to solve this problem by reduce it to the integral equation for first kind. The Boundary value problem can be formulated as an integral first kind equations. The discretization algorithm applied to reformulated the problem as linear operator problem as matrix and vectors form. Then, Lavrentev regularization method used to find the approximation solution.