Abstract
Why are we interested in knowing that a numerical approximation of a partial differential equation is stable? It is clearly of interest to know whether the approximate solution is close to the exact solution. One way of formulating this is to require that the approximate solution converge to the exact solution in the limit of small time steps and node spacings. In this case there is however a theorem stating the equivalence between convergence and stability for consistent schemes (see i.e. Richtmyer and Morton, 1967).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin, Heidelberg
About this chapter
Cite this chapter
Kinnmark, I. (1986). Stability. In: The Shallow Water Wave Equations: Formulation, Analysis and Application. Lecture Notes in Engineering, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82646-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-82646-7_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16031-1
Online ISBN: 978-3-642-82646-7
eBook Packages: Springer Book Archive