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Pointwise inclusions of fixed points by finite dimensional iteration schemes

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Summary

Finite dimensional iteration schemes which provide pointwise bounds for the solutions of nonlinear integral equations are considered. The method is based on a discretization technique which takes advantage of apriori known structure properties of the solutions. The resulting iteration can be carried out on a computer for as many steps as desired. Its high degree of accuracy is shown by numerical examples.

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Sprekels, J., Voss, H. Pointwise inclusions of fixed points by finite dimensional iteration schemes. Numer. Math. 32, 381–392 (1979). https://doi.org/10.1007/BF01401042

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