Finite difference method with cubic spline for solving nonlinear schrödinger equation

M.S. Ismail

doi:10.1080/00207169608804528

ScienceGate Book Chapters

JOURNAL ARTICLE

Finite difference method with cubic spline for solving nonlinear schrödinger equation

M.S. Ismail

Year: 1996 Journal: International Journal of Computer Mathematics Vol: 62 (1-2)Pages: 101-112 Publisher: Taylor & Francis

DOI: 10.1080/00207169608804528

Get Full-Text PDF Get Analytical Report

Abstract

In this paper we solve the nonlinear Schrödinger equation by discretizing the time derivative using finite difference method and the space derivative using cubic spline. We have proved that the resulting scheme is unconditionally stable and conserves energy.

Keywords:

Mathematics Monotone cubic interpolation Discretization Split-step method Nonlinear Schrödinger equation Mathematical analysis Nonlinear system Finite difference Finite difference method Derivative (finance) Finite difference coefficient Schrödinger equation Spline (mechanical) Applied mathematics Second derivative Partial differential equation Finite element method Mixed finite element method Physics Polynomial Quantum mechanics

Metrics

Cited By

0.44

FWCI (Field Weighted Citation Impact)

Refs

0.65

Citation Normalized Percentile

Is in top 1%

Is in top 10%

Citation History

Topics

Numerical methods for differential equations

Physical Sciences → Mathematics → Numerical Analysis

Model Reduction and Neural Networks

Physical Sciences → Physics and Astronomy → Statistical and Nonlinear Physics

Electromagnetic Simulation and Numerical Methods

Physical Sciences → Engineering → Electrical and Electronic Engineering

Finite difference method with cubic spline for solving nonlinear schrödinger equation

Abstract

Metrics

Citation History

Topics

Related Documents

Solving coupled nonlinear Schrödinger equation using finite difference method and hybrid cubic B-spline collocation method

Solving the nonlinear Schrödinger equation using cubic B-spline interpolation and finite difference methods

A finite-difference method for solving the cubic Schrödinger equation

Solving the nonlinear Schrödinger equation using cubic B-spline interpolation and finite difference methods on dual solitons

A quadratic B-spline finite element method for solving nonlinear Schrödinger equation