Abstract
We want to solve numerically the functional equation F(y)=o. For that purpose we use a discretization method with the property that the global discretization error admits an asymptotic expansion. We combine this with Newton's method and find numerical methods which are related to Pereyra's technique [8]. The first step of these methods have been given for the special case of initial value problems for ordinary differential equations by Zadunaisky [14,15] and Stetter [12].
This report was partially supported by a grant of the Volks-Wagen-Foundation.
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Böhmer, K. (1976). A defect correction method for functional equations. In: Schaback, R., Scherer, K. (eds) Approximation Theory. Lecture Notes in Mathematics, vol 556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087394
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DOI: https://doi.org/10.1007/BFb0087394
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