New stable method to solve heat conduction problems in extremely large systems

08/24/2019

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by   Endre Kovács, et al.

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We present a new explicit and stable numerical algorithm to solve the homogeneous heat equation. We illustrate the performance of the new method in the cases of two 2D systems with highly inhomogeneous random parameters. Spatial discretization of these problems results in huge and stiff ordinary differential equation systems, which can be solved by our novel method faster than by explicit or the commonly used implicit methods.