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Numerical Solution of Nonlinear Integro-Differential Equations with Initial Conditions by Bernstein Operational Matrix of Derivative
Department of Mathematics, Islamic Azad University of Birjand, Birjand, Iran
Department of Mathematics, Islamic Azad University of Birjand, Birjand, Iran
- 1 Department of Mathematics, Islamic Azad University of Birjand, Birjand, Iran
- 2 Department of Mathematics, Islamic Azad University of Birjand, Birjand, Iran
International Journal of Modern Nonlinear Theory and Application·Volume 02 (2013)·Pages 141–149·Published 13 June 2013·DOI10.4236/ijmnta.2013.22018
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Abstract
In this paper, we present a practical matrix method for solving nonlinear Volterra-Fredholm integro-differential equations under initial conditions in terms of Bernstein polynomials on the interval [0,1]. The nonlinear part is approximated in the form of matrices’ equations by operational matrices of Bernstein polynomials, and the differential part is approximated in the form of matrices’ equations by derivative operational matrix of Bernstein polynomials. Finally, the main equation is transformed into a nonlinear equations system, and the unknown of the main equation is then approximated. We also give some numerical examples to show the applicability of the operational matrices for solving nonlinear Volterra-Fredholm integro-differential equations (NVFIDEs).
KeywordsBernstein PolynomialOperational MatrixIntegro-Differential Equations
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