NDLI: On the implementation of boundary conditions for the method of lines

Content Provider	Springer Nature Link
Author	Gustafsson, Bertil
Copyright Year	1998
Abstract	The method of lines for difference approximations of hyperbolic first order systems of partial differential equations is analyzed. The approximations are based on strictly semibounded difference operators including high order ones. The formulation of the ODE-system requires that the implementation of the boundary conditions is done carefully. We shall illustrate how different ways of implementation give rise to different stability properties. In particular, we derive a way of implementation that leads to an approximation that is strongly stable.It has been an open problem, whether for semidiscrete approximations with this strong stability property, the timestep for the ODE-solver is governed by the Cauchy problem. We present a counterexample showing that it is not.The analysis presented in this paper also serves as an illustration of the significant difference between different stability concepts.
Ending Page	314
Page Count	22
Starting Page	293
File Format	PDF
ISSN	00063835
e-ISSN	15729125
Journal	BIT Numerical Mathematics
Issue Number	2
Volume Number	38
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	1998-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Stability and convergence of numerical methods Hyperbolic system Computational Mathematics and Numerical Analysis Numeric Computing Method of lines Mathematics boundary conditions difference approximation method of lines
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Networks and Communications Computational Mathematics Software

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