Finite Difference Schemes on unbounded Domains
Please always quote using this URN:urn:nbn:de:0296-matheon-2211
- We discuss the nonstandard problem of using the finite difference method to solve numerically a partial differential equation posed on an unbounded domain. We propose different strategies to construct so-called discrete articial boundary conditions (ABCs) and present an efficient implementation by the sum-of-exponential ansatz. The derivation of the ABCs is based on the knowledge of the exact solution, the construction of asymptotic solutions or the usage of a continued fraction expansion to a second-order difference equation. Our approach is explained by means of three different types of partial differential equations arising in option pricing, in quantum mechanics and in (underwater) acoustics. Finally, we conclude with an illustrating numerical example from underwater acoustics showing the superiority of our new approach.
Author: | Matthias Ehrhardt |
---|---|
URN: | urn:nbn:de:0296-matheon-2211 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2005/03/02 |
Release Date: | 2005/03/02 |
Institute: | Technische Universität Berlin |
Preprint Number: | 213 |