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A Hermite collocation method for the approximate solutions of high-order linear Fredholm integro-differential equations. (English) Zbl 1228.65240

Summary: A Hermite matrix method is presented to solve high-order linear Fredholm integro-differential equations with variable coefficients under the mixed conditions in terms of the Hermite polynomials. The proposed method converts the equation and its conditions to matrix equations, which correspond to a system of linear algebraic equations with unknown Hermite coefficients, by means of collocation points on a finite interval. Then, by solving the matrix equation, the Hermite coefficients and the polynomial approach are obtained. Also, examples that illustrate the pertinent features of the method are presented; the accuracy of the solutions and the error analysis are performed.

MSC:

65R20 Numerical methods for integral equations
45B05 Fredholm integral equations
45J05 Integro-ordinary differential equations
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References:

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