### Abstract

Finite element method with a posteriori estimation using interval arithmetic is discussed for a Fredholm integral equation of the second kind. This approach is general. It leads to the guaranteed L asymptotically exact estimate without the usual overestimation when interval arithmetic is used. An algorithm is provided for determination of an approximate solution such that the computed error bound between the exact solution and its approximation in L is less than the given tolerance . Numerical solution for the equation with only C1 kernel illustrates the approach.

Original language | English |
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Pages (from-to) | 549-566 |

Number of pages | 18 |

Journal | International Journal of Computer Mathematics |

Volume | 86 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2009 Mar 1 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics
- Computer Science Applications
- Computational Theory and Mathematics

### Cite this

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*International Journal of Computer Mathematics*, vol. 86, no. 3, pp. 549-566. https://doi.org/10.1080/00207160802624729

**Interval arithmetic error estimation for the solution of Fredholm integral equation.** / Babuška, Ivo; Liu, Kang-Man.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Interval arithmetic error estimation for the solution of Fredholm integral equation

AU - Babuška, Ivo

AU - Liu, Kang-Man

PY - 2009/3/1

Y1 - 2009/3/1

N2 - Finite element method with a posteriori estimation using interval arithmetic is discussed for a Fredholm integral equation of the second kind. This approach is general. It leads to the guaranteed L asymptotically exact estimate without the usual overestimation when interval arithmetic is used. An algorithm is provided for determination of an approximate solution such that the computed error bound between the exact solution and its approximation in L is less than the given tolerance . Numerical solution for the equation with only C1 kernel illustrates the approach.

AB - Finite element method with a posteriori estimation using interval arithmetic is discussed for a Fredholm integral equation of the second kind. This approach is general. It leads to the guaranteed L asymptotically exact estimate without the usual overestimation when interval arithmetic is used. An algorithm is provided for determination of an approximate solution such that the computed error bound between the exact solution and its approximation in L is less than the given tolerance . Numerical solution for the equation with only C1 kernel illustrates the approach.

UR - http://www.scopus.com/inward/record.url?scp=61449239056&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=61449239056&partnerID=8YFLogxK

U2 - 10.1080/00207160802624729

DO - 10.1080/00207160802624729

M3 - Article

VL - 86

SP - 549

EP - 566

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

SN - 0020-7160

IS - 3

ER -