Numerical Clifford Analysis for Nonlinear Schrodinger Problem

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.

This article has 6 figures. This article has benn accepted for publication in the Journal of Numerical Methods for Partial Differential Equations

References in corpus (2)

• Quaternionic factorization of the Schroedinger operator and its applications to some first order systems of mathematical physics
• Factorization of the Non-Stationary Schrodinger Operator

Cited by in corpus (3)

• On fractional semidiscrete Dirac operators of Lévy-Leblond type
• Relativistic Wave Equations on the lattice: an operational perspective
• On a correspondence principle between discrete differential forms, graph structure and multi-vector calculus on symmetric lattices