ISSN:
1572-9125
Keywords:
65M12
;
65L20
;
65M70
;
stability of numerical processes
;
initial(-boundary) value problems
;
ordinary and partial differential equations
;
one-step and multistep methods
;
spectral collocation methods
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper is concerned with the stability of numerical processes for solving initial value problems. We present a stability result which is related to a well-known theorem by von Neumann, but the requirements to be satisfied are less severe and easier to verify. As an illustration we consider a simple convection-diffusion equation. For the spatial discretization we use a spectral collocation method (based on so-called Legendre-Gauss-Lobatto points). We show that the fully discretized numerical process is stable, provided that the temporal step size is bounded by a constant depending only on the convection-diffusion equation, the number of collocation points and the time-stepping method under consideration.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01955870
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