Staggered Time Integrators for Wave Equations

We consider variations of the Adams-Bashforth, backward differentiation, and Runge-Kutta families of time integrators to solve systems of linear wave equations on uniform, time-staggered grids. These methods are found to have smaller local truncation errors and to allow larger stable time steps than...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2001-01, Vol.38 (3), p.718-741
Main Authors: Ghrist, Michelle, Fornberg, Bengt, Driscoll, Tobin A.
Format: Article
Language:English
Subjects:
Accuracy
Applied mathematics
Coefficients
Constant coefficients
Error rates
Integration tables
Mathematical constants
Methods
Ordinary differential equations
Polynomials
Stencils
Truncation errors
Wave equations
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Description
Summary:We consider variations of the Adams-Bashforth, backward differentiation, and Runge-Kutta families of time integrators to solve systems of linear wave equations on uniform, time-staggered grids. These methods are found to have smaller local truncation errors and to allow larger stable time steps than traditional nonstaggered versions of equivalent orders. We investigate the accuracy and stability of these methods analytically, experimentally, and through the use of a novel root portrait technique.
ISSN:0036-1429
1095-7170
DOI:10.1137/S0036142999351777