Testing and comparing the performance of numerical methods for the heat conduction equation partial differential equation

Absztrakt

This research collected 12 numerical algorithms that solve the transient diffusion equation with Dirichlet boundary conditions in one space dimension. Some of these methods are explicit and unconditionally stable simultaneously. A nontrivial analytical solution, recently obtained by a self-similar Ansatz, served as the reference solution. The errors were calculated and plotted as a function of the time step size and execution times. The conclusion is that there are explicit and stable methods that provide acceptable results faster than the traditional Runge-Kutta style methods.