D-iteration: application to differential equations

TL;DR

This paper explores the application of the D-iteration algorithm to numerically solve differential equations like the heat equation in multiple dimensions, offering an alternative to traditional iterative methods.

Contribution

It introduces a novel application of the D-iteration algorithm for solving differential equations, extending its use beyond its typical domain.

Findings

Demonstrates the effectiveness of D-iteration for 2D and 3D heat equations

Shows compatibility with Gauss-Seidel based problem classes

Provides a new iterative approach for differential equation solutions

Abstract

In this paper, we study how the D-iteration algorithm can be applied to numerically solve the differential equations such as heat equation in 2D or 3D. The method can be applied on the class of problems that can be addressed by the Gauss-Seidel iteration, based on the linear approximation of the differential equations.