A spectral method for solving an inverse time-dependent source problem

In this paper, a numerical algorithm based on Chebyshev polynomials is presented for recovering the unknown timedependent source term and obtaining a solution of the inverse problem. For solving the problem, the operational matrices of integration and derivation are utilized to reduce the mentioned problem into the matrix equations which correspond to a system of linear equations with unknown Chebyshev coefficients. Finally, anumerical example will be presented to illustrate the ability and efficiency of theintroduced scheme.

Keywords:

Inverse problem , Nonhomogenous parabolic equation , time-dependent source term , Chebyshev polynomials , Operational matrix