### Abstract

Language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | Department of Applied Mathematics, University of Twente |

Number of pages | 15 |

State | Published - Jan 2012 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
---|---|

Publisher | University of Twente, Department of Applied Mathematics |

No. | 1973 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Keywords

- MSC-65F60
- MSC-65F30
- MSC-65M22
- MSC-65M20
- EWI-21277
- Unconditionally stable time integration
- Proper orthogonal decomposition
- Truncated SVD
- Exponential residual
- Matrix exponential
- Block Krylov subspace methods
- Exponential time integration
- IR-79354
- MSC-65L05
- METIS-285233

### Cite this

*A block Krylov subspace time-exact solution method for linear ODE systems*. (Memorandum / Department of Applied Mathematics; No. 1973). Enschede: Department of Applied Mathematics, University of Twente.

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*A block Krylov subspace time-exact solution method for linear ODE systems*. Memorandum / Department of Applied Mathematics, no. 1973, Department of Applied Mathematics, University of Twente, Enschede.

**A block Krylov subspace time-exact solution method for linear ODE systems.** / Bochev, Mikhail A.

Research output: Book/Report › Report

TY - BOOK

T1 - A block Krylov subspace time-exact solution method for linear ODE systems

AU - Bochev,Mikhail A.

N1 - The author's surname can also be spelled as "Bochev"

PY - 2012/1

Y1 - 2012/1

N2 - We propose a time-exact Krylov-subspace-based method for solving linear ODE (ordinary differential equation) systems of the form $y'=-Ay + g(t)$ and $y''=-Ay + g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of the source term $g(t)$, constructed with the help of the truncated SVD (singular value decomposition). The second stage is a special residual-based block Krylov subspace method. The accuracy of the method is only restricted by the accuracy of the piecewise polynomial approximation and by the error of the block Krylov process. Since both errors can, in principle, be made arbitrarily small, this yields, at some costs, a time-exact method. Numerical experiments are presented to demonstrate efficiency of the new method, as compared to an exponential time integrator with Krylov subspace matrix function evaluations.

AB - We propose a time-exact Krylov-subspace-based method for solving linear ODE (ordinary differential equation) systems of the form $y'=-Ay + g(t)$ and $y''=-Ay + g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of the source term $g(t)$, constructed with the help of the truncated SVD (singular value decomposition). The second stage is a special residual-based block Krylov subspace method. The accuracy of the method is only restricted by the accuracy of the piecewise polynomial approximation and by the error of the block Krylov process. Since both errors can, in principle, be made arbitrarily small, this yields, at some costs, a time-exact method. Numerical experiments are presented to demonstrate efficiency of the new method, as compared to an exponential time integrator with Krylov subspace matrix function evaluations.

KW - MSC-65F60

KW - MSC-65F30

KW - MSC-65M22

KW - MSC-65M20

KW - EWI-21277

KW - Unconditionally stable time integration

KW - Proper orthogonal decomposition

KW - Truncated SVD

KW - Exponential residual

KW - Matrix exponential

KW - Block Krylov subspace methods

KW - Exponential time integration

KW - IR-79354

KW - MSC-65L05

KW - METIS-285233

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - A block Krylov subspace time-exact solution method for linear ODE systems

PB - Department of Applied Mathematics, University of Twente

CY - Enschede

ER -