Crank-Nicolson finite difference scheme for the Rosenau-Burgers equation
type: Item
instance of: scholarly article
title: Crank-Nicolson finite difference scheme for the Rosenau-Burgers equation
zbMATH Open document ID: 1166.65041
author: Bing Hu
author: Youcai Xu
author: Jinsong Hu
published in: Applied Mathematics and Computation
publication date: 2009-01-14T00:00:00Z
review text: The authors consider an initial-boundary value problem of Rosenau-Burgers equation \[ u_{t}+u_{xxxxt}-u_{xx}+u_{x}+uu_{x}=0 \] and propose a Crank-Nicolson type finite difference scheme. The existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is stable and convergent in the order of \( O(\Delta t^{2}+\Delta x^{2})\). The method is tested by an example. It will be better if the new scheme is tested by a shock wave problem.
reviewed by: Weizhong Dai
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 5491031
zbMATH Keywords: Rosenau-Burgers equation
zbMATH Keywords: Crank-Nicolson scheme
zbMATH Keywords: convergence
zbMATH Keywords: stability
zbMATH Keywords: numerical example
zbMATH Keywords: finite difference scheme
MaRDI profile type: Publication
full work available at URL: j.amc.2008.06.051
OpenAlex ID: W2087482131
cites work: Q3211724
cites work: Finite Difference Approximate Solutions for
cites work: Numerical methods for the rosenau equation
cites work: A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation
cites work: Q4222507
cites work: Asymptotic behavior of solutions to the Rosenau-Burgers equation with a periodic initial boundary
cites work: A better asymptotic profile of Rosenau-Burgers equation
cites work: Q5691466
cites work: Long-time behaviour of solution for rosenau-burgers equation(II)
cites work: Q5435864
cites work: Q5522517
DOI: 10.1016/J.AMC.2008.06.051
description: scientific article