Comprehensive investigation of the explicit, positivity preserving methods for the heat equation

Part 1

Szerzők

  • Khayrullaev Husniddin University of Miskolc
  • Kovács Endre University of Miskolc

DOI:

https://doi.org/10.35925/j.multi.2024.1.5

Kulcsszavak:

explicit numerical methods, unconditional stability, heat equation, parabolic PDEs

Absztrakt

In this paper-series, we investigate the performance of 12 explicit non-conventional algorithms. All of them have the convex combination property, thus they are unconditionally stable and preserve the positivity of the solution when they applied to the heat equation. In this part of the series, we construct several 2D systems to find how the errors depend on the time step size. Sweeps for other key parameters will be presented in the next part of the series.

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Megjelent

2024-04-25