Numerical integration of \((2+1)\) dimensional PDEs for \(S^2\) valued functions
type: Item
instance of: scholarly article
title: Numerical integration of \((2+1)\) dimensional PDEs for \(S^2\) valued functions
zbMATH Open document ID: 0910.65062
published in: Journal of Computational Physics
publication date: 1999-04-12T00:00:00Z
review text: The authors compare differential numerical methods of studying the time evolution of partial differential equations (PDEs) in the \((2+1)\)-dimensional \(S^2\) sigma model. They use three different methods to describe the fields: a unit length vector, the polar angles, and a complex field. For the time integration, they employ both a fourth-order Runge-Kutta method and the leapfrog method. For each formulation, they tackle the problems created by the field description and develop a stable method to solve the equations satisfied by the fields. They compare the results of all methods, focussing their attention on the accuracy of the results and the computing requirement.
reviewed by: Ziwen Jiang
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35K30
zbMATH DE Number: 1212281
zbMATH Keywords: finite difference
zbMATH Keywords: stability
zbMATH Keywords: comparison of methods
zbMATH Keywords: Runge-Kutta method
zbMATH Keywords: leapfrog method
author: B. Piette
author: Wojciech J. Zakrzewski
MaRDI profile type: Publication
full work available at URL: jcph.1998.6013
OpenAlex ID: W2002704211
cites work: Soliton scatterings in some relativistic models in (2+1) dimensions
cites work: Shrinking of solitons in the (2 + 1)-dimensional sigma model
cites work: Multi-soliton dynamics in the Skyrme model
cites work: Soliton scattering in the Skyrme model in (2+1) dimensions. II. More general systems
cites work: Dynamics of baby skyrmions
cites work: Local theory of solutions for the \(0(2k+1)\sigma\)-model
cites work: Soliton stability in the O(3) sigma -model in (2+1) dimensions
DOI: 10.1006/JCPH.1998.6013
description: scientific article; zbMATH DE number 1212281