Nonlinear scheme with high accuracy for nonlinear coupled parabolic-hyperbolic system
type: Item
instance of: scholarly article
title: Nonlinear scheme with high accuracy for nonlinear coupled parabolic-hyperbolic system
zbMATH Open document ID: 1218.65082
author: Xia Cui
author: Jing-yan Yue
author: Guangwei Yuan
published in: Journal of Computational and Applied Mathematics
publication date: 2011-05-17T00:00:00Z
review text: The authors construct an unconditionally stable nonlinear three-level scheme with second-order \(H^1\)- and \(L^2\)-norm accuracy in temporal and spatial variables, respectively, for two-dimensional nonlinear parabolic-hyperbolic systems. The stability and convergence properties of this scheme are rigorously studied. Difficulties arising from the nonlinearity and coupling between parabolic and hyperbolic equations are overcome by an ingenious use of the method of energy estimation and inductive hypothesis reasoning. This method differs from those used for linear schemes and can be adopted to perform strict theoretical analysis of other nonlinear schemes for nonlinear partial differential equation problems. Numerical tests verify the theoretical results.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35M13
zbMATH DE Number: 5895480
zbMATH Keywords: nonlinear
zbMATH Keywords: coupled parabolic-hyperbolic system
zbMATH Keywords: high accuracy
zbMATH Keywords: unconditional stability
zbMATH Keywords: numerical examples
zbMATH Keywords: finite difference method
zbMATH Keywords: convergence
zbMATH Keywords: method of energy estimation
MaRDI profile type: Publication
full work available at URL: j.cam.2011.02.008
OpenAlex ID: W2076152441
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DOI: 10.1016/J.CAM.2011.02.008
description: scientific article; zbMATH DE number 5895480