New stable, explicit, second-order method to solve non-stationary heat conduction problems

Abstract

In this short note, we present a fundamentally new explicit and stable numerical algorithm to solve the spatially discretized linear heat or diffusion equation. Unlike conventional explicit methods (like Runge-Kutta) it uses a non-polynomial expression of the timestep-size to calculate the new values of the variable. We compare the performance of the new method with numerical solutions. According to our investigations, the method is second order in time and it is faster than the commonly used explicit or implicit methods, especially in the case of extremely large stiff systems.