New stable, explicit, first order method to solve the heat conduction equation

Kovács, Endre (2020) New stable, explicit, first order method to solve the heat conduction equation. JOURNAL OF COMPUTATIONAL AND APPLIED MECHANICS, 15 (1). pp. 3-13. ISSN 1586-2070

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Abstract

In this paper a novel explicit and unconditionally stable numerical algorithm is introduced to solve the inhomogeneous non-stationary heat or diffusion equation. Spatial discretization of these problems usually yields huge and stiff ordinary differential equation systems, the solution of which is still time-consuming. The performance of the new method is compared with analytical and numerical solutions. It is proven exactly as well as demonstrated numerically that the new method is first order in time and can give approximate results for extremely large systems faster than the commonly used explicit or implicit methods. The new method can be easily parallelized and it is handy to apply regardless of space dimensions and grid irregularity.

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