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Generalized disks of contractivity for explicit and implicit runge-kutta methods
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Dahlquist, G. Jeltsch, R. |
| Copyright Year | 1979 |
| Description | The A-contractivity of Runge-Kutta methods with respect to an inner product norm was investigated thoroughly by Butcher and Burrage (who used the term B-stability). Their theory is extended to contractivity in a region bounded by a circle through the origin. The largest possible circle is calculated for many known explicit Runge-Kutta methods. As a rule it is considerably smaller than the stability region, and in several cases it degenerates to a point. It is shown that an explicit Runge-Kutta method cannot be contractive in any circle of this class if it is more than fourth order accurate. |
| File Size | 636768 |
| Page Count | 23 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19790024769 |
| Archival Resource Key | ark:/13960/t09w57x4c |
| Language | English |
| Publisher Date | 1979-01-01 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Boundary Value Problems Nonlinear Equations Continuity Mathematics Theorem Proving Differential Equations Runge-kutta Method Disks Numerical Stability 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 |
