A method based on the SCT to solve the inverse problem for heat equation

Abstract

In this article, a mathematical model of the inverse problem is considered. Based on this model a formulation of inverse problem for heat equation is proposed. Shifted Chebyshev Tau (SCT) method is suggested to solve the inverse problem. The aim of this determined effort is to identify unknown function and unknown control parameter of the mathematical model. In order to achieve highly accurate solution to this problem, the operational matrix of shifted Chebyshev polynomials is investigated in conjunction with tau scheme. To demonstrate the validity and applicability of the developed scheme, numerical example is presented.