Interval arithmetic error estimation for the solution of Fredholm integral equation

Ivo Babuška, Kang-Man Liu

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)549-566
Number of pages18
JournalInternational Journal of Computer Mathematics
Volume86
Issue number3
DOIs
Publication statusPublished - 2009 Mar 1

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Interval Arithmetic
Fredholm Integral Equation
Error Estimation
Error analysis
Integral equations
Finite element method
Error Bounds
Tolerance
Approximate Solution
Exact Solution
Finite Element Method
Numerical Solution
kernel
Approximation
Estimate

All Science Journal Classification (ASJC) codes

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

Cite this

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

In: International Journal of Computer Mathematics, Vol. 86, No. 3, 01.03.2009, p. 549-566.

Research output: Contribution to journalArticle

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