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

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