Extension of the operational Tau method for solving 1-D nonlinear transient heat conduction equations

In this paper, we consider a class of nonlinear transient heat conduction equations with some supplementary conditions. We apply the operational Tau method with arbitrary polynomial bases to approximate the solution of these equations. In addition, some theoretical results are given to simplify and reduce the computational cost. Finally some numerical examples are given to clarify the efficiency and accuracy of the proposed method.