A direct Numerov sixth order numerical scheme to accurately solve the unidimensional Poisson equation with Dirichlet boundary conditions

TL;DR

This paper introduces a sixth-order Numerov-based numerical scheme for efficiently solving the one-dimensional Poisson equation with Dirichlet boundary conditions, enhancing accuracy and computational speed for physics simulations.

Contribution

The paper presents a novel sixth-order Numerov scheme that is both highly accurate and computationally efficient for solving 1D Poisson equations with Dirichlet conditions.

Findings

Achieves sixth-order accuracy in numerical solutions.

Maintains linear computational complexity with grid size.

Improves numerical codes in solid state physics applications.

Abstract

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.