Computable Bounds for Solutions of Integral Equations.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Interval integration is used to obtain inclusions of integral operators of the form gus integral of Tgs,t,us,utdt which can be carried out on a computer. The resulting inclusions, combined with interval iteration, are used to compute guaranteed upper and lower bounds for solutions of integral equations of the form u gu for s is an element of S. It is also possible to establish existence or nonexistence of solutions of integral equations in given regions on the basis of results of the computation. Examples of applications of this technique to linear and nonlinear integral equations are eigenvalue problems for linear integral operators are given. Keywords Integral equations Eigenvalue problems Error bounds Interval integration, Interval iteration.
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