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We deal with an efficient approach for the complete error control in scientific computing. For results obtained by standard numerical routines we provide in an additional validation step existence and... enclosure of the corresponding solutions. The basic ideas of these methods are derived exemplary for nonlinear Volterra equations and then generalized to various initial value problems. We combine principles from functional analysis and enclosure theory to determine realistic and reliable a posteriori error bounds for numerical approximations. This method has been applied successfully to various problems.続きを見る
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