Abstract
A complete or total absolute error Δ for the approximate solution of Volterra integral equations of the second and the first kind is considered. This error is less or equal to the sum of errors of three types because of: input data inaccuracy and incompleteness (inherent error), approximate algorithms (method error), and realization of algorithms on computers (round-off error). The optimal numerical methods with pre-assigned accuracy allowing us to obtain Δ < ε, where ε > 0 and pre-assigned, are determined. The minimal in order numbers of necessary basic computers’ operations under realization of the methods and the respective algorithms are estimated. And also namely those equations and methods for which the numbers of operations are admissible in practice under rather small ε are investigated.
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Ivanov, V.V. (1999). Solution of Volterra Equations with Pre-Assigned Accuracy. In: Model Development and Optimization. Applied Optimization, vol 28. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4062-5_5
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DOI: https://doi.org/10.1007/978-1-4615-4062-5_5
Publisher Name: Springer, Boston, MA
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