Numerical Clifford Analysis for Nonlinear Schrodinger Problem

TL;DR

This paper develops a numerical method combining Clifford analysis and finite differences to solve the nonlinear Schrödinger equation, demonstrating convergence and providing numerical examples.

Contribution

It introduces a novel numerical scheme using Witt basis and finite differences for the nonlinear Schrödinger problem, including a discrete fundamental solution and convergence proof.

Findings

Convergence of the proposed numerical scheme is established.

A discrete fundamental solution for the non-stationary Schrödinger operator is constructed.

Numerical examples validate the effectiveness of the method.

Abstract

The aim of this work is to study the numerical solution of the nonlinear Schrodinger problem using a combination between Witt basis and finite difference approximations. We construct a discrete fundamental solution for the non-stationary Schrodinger operator and we show the convergence of the numerical scheme. Numerical examples are given at the end of the paper.