Testing of stable, explicit and implicit numerical algorithms for conductive heat conduction problems

Abstract

In this work, we present and compare recently published explicit and stable methods with each other and an explicit and some implicit methods which are known from the literature for solving the heat conduction equation.  We examined the convergence and computational performance properties of these methods by performing case studies on two-dimensional inhomogeneous systems generated using random numbers. Numerical case studies which we performed on a moderately stiff system, and even on a strongly anisotropic system showed that the explicit numerical methods outperform to the widely used implicit methods.