New stable, explicit, first order method to solve the heat conduction equation

TL;DR

This paper presents a new explicit, stable, first-order numerical method for solving the heat conduction equation that outperforms traditional methods in large systems by providing faster approximate solutions.

Contribution

The paper introduces a novel explicit and stable first-order method for heat equation simulation, improving speed for large systems compared to existing methods.

Findings

Method is first order in time.

Provides accurate approximations for large systems.

Faster than traditional explicit or implicit methods.

Abstract

We introduce a novel explicit and stable numerical algorithm to solve the spatially discretized heat or diffusion equation. We compare the performance of the new method with analytical and numerical solutions. We show that the method is first order in time and can give approximate results for extremely large systems faster than the commonly used explicit or implicit methods.