## Abstract

We present constructive a posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations (ODEs) on a bounded interval. Here, "constructive" indicates that we can obtain bounds of the operator norm in which all constants are explicitly given or are represented in a numerically computable form. In general, it is difficult to estimate these inverse operators a priori. We, therefore, propose a technique for obtaining a posteriori estimates by using Galerkin approximation of inverse operators. This type of estimation will play an important role in the numerical verification of solutions for initial value problems in nonlinear ODEs as well as for parabolic initial boundary value problems.

Original language | English |
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Pages (from-to) | 1622-1636 |

Number of pages | 15 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 236 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2011 Oct 15 |

Externally published | Yes |

## Keywords

- Constructive a posteriori estimates
- Finite element method
- Linear ODEs

## ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics