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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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##### References:
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