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Bernstein Polynomial Approach for Solution of Higher-Order Mixed Linear Fredholm Integro-Differential-Difference Equations with Variable Coefficients

TWMS Journal of Pure and Applied Mathematics, Vol. 7, No. 1, 2016, 46-62.

Bernstein collocation matrix method is presented to solve m-th order linear Fredholm integro-differential-difference equations subjected to mixed conditions. The methodology is based on approximation by the truncated Bernstein series, which converts the given equation and the conditions into a system of linear algebraic equations with Bernstein coefficients. By solving the arising system, the Bernstein coefficients of the solution can be obtained. The method is also valid for any combination of differential, difference, differential-difference and Fredholm integral equations. The applicability and validity of the proposed scheme is demon-strated by numerical experiments and comparative analysis of the results is given too.

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