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Numerical piecewise approximate solution of Fredholm integro-differential equations by the tau method. (English) Zbl 1099.65136
Summary: A general form of numerical piecewise approximate solution of linear integro-differential equations of Fredholm type is discussed. It is formulated for using the operational tau method to convert the differential part of a given integro-differential equation (IDE) to its matrix representation. This formulation of the tau method can be useful for such problems over long intervals and also can be used as a good and simple alternative algorithm for other piecewise approximations such as splines or collocation. A tau error estimator is also adapted for piecewise application of the tau method. Some numerical examples are considered to demonstrate the implementation and general effect of application of this (segmented) piecewise Chebyshev tau method.

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
Full Text: DOI
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