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Propagation and stability of wavelike solutions of finite difference equations with variable coefficients

Michael B. Giles, +1 more
- 15 May 1985 - 
- Vol. 58, Iss: 3, pp 349-360
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TLDR
In this paper, the propagation and dissipation of wave solutions to finite difference equations are analyzed on the basis of an asymptotic approach in which a wave solution is expressed as a product of a complex amplitude and an oscillatory phase function whose frequency and wavenumber may also be complex.
About: 
This article is published in Journal of Computational Physics.The article was published on 1985-05-15 and is currently open access. It has received 29 citations till now. The article focuses on the topics: Dispersion relation & Group velocity.

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Book

Atmospheric Modeling, Data Assimilation and Predictability

Eugenia Kalnay
TL;DR: A comprehensive text and reference work on numerical weather prediction, first published in 2002, covers not only methods for numerical modeling, but also the important related areas of data assimilation and predictability.
Journal ArticleDOI

Atmospheric Modeling, Data Assimilation, and Predictability

Christopher K. Wikle
- 01 Nov 2005 - 
TL;DR: This monograph is an outstanding monograph on current research on skewelliptical models and its generalizations and does an excellent job presenting the depth of methodological research as well as the breath of application regimes.
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Development of High-Order Taylor-Galerkin Schemes for LES

Olivier Colin, +1 more
- 10 Aug 2000 - 
TL;DR: The implementation and development of a new Taylor?Galerkin finite-element scheme within an unstructured/hybrid, parallel solver for unsteady LES is described, which is third-order in space and time and has a low dissipative error.
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A Finite-Difference GCM Dynamical Core with a Variable-Resolution Stretched Grid

Michael S. Fox-Rabinovitz, +3 more
- 01 Nov 1997 - 
TL;DR: In this paper, a finite-difference dynamical core using variable resolution, or stretched grids, is developed and used for regional-global medium-term and long-term integrations, where a significant downscaling is taking place over the area of interest, due to better-resolved regional fields and boundary forcings.
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Developments and trends in three-dimensional mesh generation

T. J. Baker
- 01 Jul 1989 - 
TL;DR: This paper reviews recent progress and emphasizes the central themes that can be expected to form a solid foundation for future developments in mesh generation.
References
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Linear and Nonlinear Waves

G. B. Whitham
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.

Linear and non linear waves

G.B. Whitham
Book

Fourier Analysis of Numerical Approximations of Hyperbolic Equations

Robert Vichnevetsky, +1 more
Journal ArticleDOI

Stability theory of difference approximations for mixed initial boundary value problems. II

Bertil Gustafsson, +2 more
- 01 Jul 1972 - 
TL;DR: Stability theory of difference approximations for mixed initial boundary value problems were studied in this article, where the authors proposed a stability theory for MIFV problems and proved its correctness.
Book

Waves in fluids

James Lighthill
TL;DR: One-dimensional waves in fluids as mentioned in this paper were used to describe sound waves and water waves in the literature, as well as the internal wave and the water wave in fluids, and they can be classified into three classes: sound wave, water wave, and internal wave.
Related Papers (5)

Group velocity interpretation of the stability theory of Gustafsson, Kreiss, and Sundström

Lloyd N. Trefethen
- 01 Feb 1983 - 

High resolution climate simulation over Europe

Michel Déqué, +1 more
- 01 Aug 1995 - 

Vertical Differencing of the Primitive Equations in Sigma Coordinates

Akio Arakawa, +1 more
- 01 Jan 1983 - 

A global numerical weather prediction model with variable resolution: Application to the shallow‐water equations

Philippe Courtier, +1 more
- 01 Jul 1988 - 

A comprehensive meteorological modeling system?RAMS

Roger A. Pielke, +10 more
- 01 Mar 1992 - 
Frequently Asked Questions (1)
Q1. What are the contributions in "Propagation and stability of wavelike solutions of finite difference equations with variable coefficients" ?

In this paper, an asymptotic approach is used to analyze the propagation and dissipation of wavelike solutions to finite difference equations.