Name
Title | ||
|---|---|---|
Strang-type preconditioners applied to ordinary and neutral differential-algebraic equations. |
Abstract | ||
|---|---|---|
This paper deals with boundary-value methods (BVMs) for ordinary and neutral differential-algebraic equations. Different from what has been done in Lei and Jin (Lecture Notes in Computer Science, vol. 1988. Springer: Berlin, 2001; 505-512), here, we directly use BVMs to discretize the equations. The discretization will lead to a nonsymmetric large-sparse linear system, which can be solved by the GMRES method. In order to accelerate the convergence rate of GMRES method, two Strang-type block-circulant preconditioners are suggested: one is for ordinary differential-algebraic equations (ODAEs), and the other is for neutral differential-algebraic equations (NDAEs). Under some suitable conditions, it is shown that the preconditioners are invertible, the spectra of the preconditioned systems are clustered, and the solution of iteration converges very rapidly. The numerical experiments further illustrate the effectiveness of the methods. Copyright (C) 2011 John Wiley & Sons, Ltd. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1002/nla.770 | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS |
Keywords | Field | DocType |
ordinary and neutral differential-algebraic equations,linear systems,Strang-type preconditioner,boundary-value methods,convergence rate | Discretization,Mathematical optimization,Linear system,Generalized minimal residual method,Mathematical analysis,L-stability,Numerical partial differential equations,Differential algebraic equation,Rate of convergence,Mathematics,Multigrid method | Journal |
Volume | Issue | ISSN |
18 | 5 | 1070-5325 |
Citations | PageRank | References |
2 | 0.51 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Chengjian Zhang | 1 | 19 | 4.04 |
| Hao Chen | 2 | 22 | 3.55 |
| Leiming Wang | 3 | 2 | 0.51 |