Fast Runge-Kutta approximation of inhomogeneous parabolic equations
Please always quote using this URN: urn:nbn:de:0297-zib-8443
- The result after $N$ steps of an implicit Runge-Kutta time discretization of an inhomogeneous linear parabolic differential equation is computed, up to accuracy $\varepsilon$, by solving only $$O\Big(\log N\, \log \frac1\varepsilon \Big) $$ linear systems of equations. We derive, analyse, and numerically illustrate this fast algorithm.
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| Author: | Maria Lopez-Fernandez, Christian Lubich, Cesar Palencia, Achim Schädle |
|---|---|
| Document Type: | ZIB-Report |
| Tag: | Runge-Kutta methods; parabolic equation |
| MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M20 Method of lines |
| Date of first Publication: | 2005/01/24 |
| Series (Serial Number): | ZIB-Report (05-10) |
| ZIB-Reportnumber: | 05-10 |
| Published in: | Appeared in: Numer. Math. 102(2005)277-291 |
