University of Tabriz Computational Methods for Differential Equations 2345-3982 8 1 2020 01 01 A Shifted Chebyshev-Tau method for finding a time-dependent heat source in heat equation 1 13 9450 10.22034/cmde.2019.9450 EN Samaneh Akbarpour Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran. Abdollah Shidfar Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran. Hashem Saberinajafi Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran. Journal Article 2018 04 20 This paper investigates the inverse problem of determining the time-dependent heat source and the temperature for the heat equation with Dirichlet boundary conditions and an integral over determination conditions. The numerical method is presented for solving the Inverse problem. Shifted Chebyshev polynomial is used to approximate the solution of the equation as a base of the tau method which is based on the Chebyshev operational matrices. The main advantage of this method is based upon reducing the partial differential equation into a system of algebraic equations of the solution. Numerical results are presented and discussed.<br />   https://cmde.tabrizu.ac.ir/article_9450_316d610f8aa0b862c298dff9ad145fab.pdf