Spatial Finite Difference Approximations for Wave-Type Equations
- 1 January 1999
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 37 (1) , 105-130
- https://doi.org/10.1137/s0036142998335881
Abstract
The simplest finite difference approximations for spatial derivatives are centered, explicit, and applied to "regular" equispaced grids. Well-established generalizations include the use of implicit (compact) approximations and staggered grids. We find here that the combination of these two concepts, together with high formal order of accuracy, is very effective for approximating the first derivatives in space that occur in many wave-type PDEs.Keywords
This publication has 13 references indexed in Scilit:
- Nonlinear Resonance Artifacts in Molecular Dynamics SimulationsJournal of Computational Physics, 1998
- Classroom Note:Calculation of Weights in Finite Difference FormulasSIAM Review, 1998
- A Practical Guide to Pseudospectral MethodsPublished by Cambridge University Press (CUP) ,1996
- Compact finite difference schemes with spectral-like resolutionJournal of Computational Physics, 1992
- High-Order Finite Differences and the Pseudospectral Method on Staggered GridsSIAM Journal on Numerical Analysis, 1990
- On the construction and efficiency of staggered numerical differentiators for the wave equationGeophysics, 1990
- COMPUTATIONAL ASPECTS OF THE CHOICE OF OPERATOR AND SAMPLING INTERVAL FOR NUMERICAL DIFFERENTIATION IN LARGE‐SCALE SIMULATION OF WAVE PHENOMENA*Geophysical Prospecting, 1987
- Highly accurate compact implicit methods and boundary conditionsJournal of Computational Physics, 1977
- On a Fourier Method for the Integration of Hyperbolic EquationsSIAM Journal on Numerical Analysis, 1975
- Higher order accurate difference solutions of fluid mechanics problems by a compact differencing techniqueJournal of Computational Physics, 1975