The DJ method for exact solutions of Laplace equation

TL;DR

This paper applies the DJ iterative method to solve Laplace equations with boundary conditions, demonstrating high accuracy and efficiency through various physical models.

Contribution

It introduces the DJ method for exact solutions of Laplace equations, showing improved accuracy and reduced calculations over existing iterative methods.

Findings

High accuracy in solving Laplace equations

Reduced computational effort compared to other methods

Effective for various physical models

Abstract

In this paper, the iterative method developed by Daftardar-Gejji and Jafari (DJ method) is employed for analytic treatment of Laplace equation with Dirichlet and Neumann boundary conditions. The method is demonstrated by several physical models of Laplace equation. The obtained results show that the present approach is highly accurate and requires reduced amount of calculations compared with the existing iterative methods.