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

Part 2


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



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


In this paper-series, we investigate the performance of 12 explicit non-conventional algorithms in several 2D systems. All of them have the convex combination property, thus they are unconditionally stable and preserve the positivity of the solution when they are applied to the heat equation. In the first part of the series, we examined how the errors depend on the time step size and running times. Now we present additional numerical test results, where sweeps for parameters such as the stiffness and the wavelength of the initial function will be performed.