A boundary residual method with heat polynomials for solving unsteady heat conduction problems

In this paper, we present a new method for solving unsteady heat conduction problems, which is based on a time–space boundary residual method with heat polynomials. More specifically, it employs an integral least squares criterion for the initial and boundary residuals so as to determine the unknown coefficients in a trial expansion of heat polynomials. Though it treats only one-dimensional cases, the present approach shows a good applicability for such heat conduction problems.