Projects / Programmes
Numerical methods for multiparameter eigenvalue problems
| Code |
Science |
Field |
Subfield |
| 1.01.03 |
Natural sciences and mathematics |
Mathematics |
Numerical and computer mathematics |
| Code |
Science |
Field |
| P170 |
Natural sciences and mathematics |
Computer science, numerical analysis, systems, control |
numerical methods, multiparameter eigenvalue problem, continuation method, Jacobi-Davidson's method
Researchers (3)
| no. |
Code |
Name and surname |
Research area |
Role |
Period |
No. of publicationsNo. of publications |
| 1. |
12066 |
PhD Janez Aleš |
Mathematics |
Researcher |
2002 - 2003 |
0 |
| 2. |
20271 |
PhD Gašper Jaklič |
Mathematics |
Researcher |
2002 - 2004 |
0 |
| 3. |
15136 |
PhD Bor Plestenjak |
Mathematics |
Head |
2002 - 2004 |
0 |
Organisations (1)
Abstract
The goal of the research is to find new and to improve the existing numerical methods for multiparameter eigenvalue problems. Problems of this type arise in a variety of applications, especially in partial differential equations of mathematical physics. Only few numerical methods are available for such problems at the moment. In particular we will examine numerical methods based on the continuation method and Jacobi-Davidson’s method. The advantage of continuation methods is that they do not require initial approximations. We will improve the methods based on the continuation method for the weakly elliptic and right definite algebraic two-parameter problems and work on methods for indefinite and multiparameter Sturm-Liouville boundary problems. Jacobi-Davidson’s type methods, which allow inexpensive calculation of a small number of eigenvalues, have been successfully applied to one-parameter problems, but have not been used for multiparameter problems yet. We will construct a Jacobi-Davidson’s type method for a right definite two-parameter problem. We will develop software libraries with implementations of new algorithms that will be available free to researchers all over the world.
