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Erdem, Kübra; Yalçinbaş, Salih; Sezer, Mehmet

A Bernoulli polynomial approach with residual correction for solving mixed linear Fredholm integro-differential-difference equations. (English) Zbl 1277.65114

J. Difference Equ. Appl. 19, No. 10, 1619-1631 (2013).
Summary: An approximate method based on Bernoulli polynomials and collocation points is presented to obtain the solutions of higher-order linear Fredholm integro-differential-difference equations with mixed conditions. The method we use consists of reducing the problem to a matrix equation which corresponds to a system of linear algebraic equations. The obtained matrix equation is based on the matrix forms of Bernoulli polynomials and their derivatives by means of collocations. The solutions are obtained as the truncated Bernoulli series which are defined in the interval \([a,b]\). To illustrate the method, it is applied to the initial and boundary values. Also, an error analysis and numerical examples are included to demonstrate the validity and applicability of the technique.

Cited in 14 Documents

MSC:

65R20 Numerical methods for integral equations
45A05 Linear integral equations
45J05 Integro-ordinary differential equations

Keywords:

Bernoulli polynomials; linear Fredholm integro-differential-difference equations; Bernoulli matrix method; collocation points; initial value problem; boundary value problem; error analysis; numerical examples
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