Title
Some Results On The Stability And Dynamics Of Finite Difference Approximations To Nonlinear Partial Differential Equations
Abstract
A miscellany of results on the nonlinear instability and dynamics of finite difference discretizations of the Burgers and Kortweg de Vries equations is obtained using a variety of phase‐plane, functional analytic, and regularity methods. For the semidiscrete (space‐discrete, time‐continuous) schemes, large‐wave‐numer instabilities occurring in special exact solutions are investigated, and parameter values for which the semidiscrete scheme is monotone are considered. For fully discrete schemes (space and time discrete), large‐wave‐number instabilities introduced by various time‐stepping schemes such as forward Euler, leapfrog, and Runge–Kutta schemes are analyzed. Also, a time step restriction for the monotonicity of the forward‐Euler time‐stepping scheme, and regularity of a 4‐stage monotone/conservative Runge–Kutta time stepping are investigated. The techniques used here may be employed, in conjunction with bifurcation‐theoretic and weakly nonlinear analyses, to analyze the stability of numerical schemes for other nonlinear partial differential equations of both dissipative and dispersive varieties. © 1993 John Wiley & Sons, Inc. Copyright © 1993 Wiley Periodicals, Inc.
Publication Date
1-1-1993
Publication Title
Numerical Methods for Partial Differential Equations
Volume
9
Issue
2
Number of Pages
117-133
Document Type
Article
Identifier
scopus
Personal Identifier
scopus
DOI Link
https://doi.org/10.1002/num.1690090203
Copyright Status
Unknown
Socpus ID
0027558621 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/0027558621
STARS Citation
Choudhury, S. Roy, "Some Results On The Stability And Dynamics Of Finite Difference Approximations To Nonlinear Partial Differential Equations" (1993). Scopus Export 1990s. 764.
https://stars.library.ucf.edu/scopus1990/764