A Finite Difference Scheme for a Class of Nonlinear Parabolic Systems in 3D Space Variables

In this paper, we establish error bound analysis for a finite-difference approximation to the solutions for a class of Nonlinear Parabolic Systems in the form (∂/∂t)v+(∂/∂x)f(v)+(∂/∂y)g(v)+(∂/∂z)h(v)=DΔv. We assume that the initial data is sufficiently smooth and of class BV. The error is proved to...

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Veröffentlicht in:	Journal of mathematical analysis and applications 1996-10, Vol.203 (2), p.490-517
1. Verfasser:	Zhao, Jennifer J.
Format:	Artikel
Sprache:	eng
Schlagworte:	Exact sciences and technology Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Partial differential equations Partial differential equations, initial value problems and time-dependant initial-boundary value problems Sciences and techniques of general use
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Zusammenfassung:	In this paper, we establish error bound analysis for a finite-difference approximation to the solutions for a class of Nonlinear Parabolic Systems in the form (∂/∂t)v+(∂/∂x)f(v)+(∂/∂y)g(v)+(∂/∂z)h(v)=DΔv. We assume that the initial data is sufficiently smooth and of class BV. The error is proved to be bounded byO(Δx\|lnΔx\|) for all positive time in an appropriate norm.
ISSN:	0022-247X 1096-0813
DOI:	10.1006/jmaa.1996.0393