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.