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A Taylor polynomial approach for solving high-order linear Fredholm integro-differential equations in the most general form. (English) Zbl 1118.65129
Summary: A Taylor method is developed for finding the approximate solution of high-order linear Fredholm integro-differential equations in the most general form under the mixed conditions. The problem is defined on the interval \([-1, 1]\) and the solution is obtained in terms of Taylor polynomials about the origin. Transforming the interval \([a, b]\) to the interval \([-1, 1]\), a problem defined on \([a, b]\) can also be solved using this method. Numerical examples are presented to illustrate the accuracy of the method.

MSC:
65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
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