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Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: an eigenvalue analysis
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Beam, Richard M. Warming, Robert F. |
| Copyright Year | 1986 |
| Description | A hyperbolic initial-boundary-value problem can be approximated by a system of ordinary differential equations (ODEs) by replacing the spatial derivatives by finite-difference approximations. The resulting system of ODEs is called a semidiscrete approximation. A complication is the fact that more boundary conditions are required for the spatially discrete approximation than are specified for the partial differential equation. Consequently, additional numerical boundary conditions are required and improper treatment of these additional conditions can lead to instability. For a linear initial-boundary-value problem (IBVP) with homogeneous analytical boundary conditions, the semidiscrete approximation results in a system of ODEs of the form du/dt = Au whose solution can be written as u(t) = exp(At)u(O). Lax-Richtmyer stability requires that the matrix norm of exp(At) be uniformly bounded for O less than or = t less than or = T independent of the spatial mesh size. Although the classical Lax-Richtmyer stability definition involves a conventional vector norm, there is no known algebraic test for the uniform boundedness of the matrix norm of exp(At) for hyperbolic IBVPs. An alternative but more complicated stability definition is used in the theory developed by Gustafsson, Kreiss, and Sundstrom (GKS). The two methods are compared. |
| File Size | 566148 |
| Page Count | 9 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19880002052 |
| Archival Resource Key | ark:/13960/t95769j3v |
| Language | English |
| Publisher Date | 1986-09-01 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Boundary Value Problems Approximation Stability Partial Differential Equations Boundary Conditions Hyperbolic Functions Cauchy Problem Finite Difference Theory Differential Equations Eigenvalues Vectors Mathematics Discrete Functions Matrices Mathematics Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
