Numerical Solution of Nonlinear Integro-Differential Equations with Initial Conditions by Bernstein Operational Matrix of Derivative

Behrooz Basirat, Mohammad Amin Shahdadi

Department of Mathematics, Islamic Azad University of Birjand, Birjand, Iran.

DOI: 10.4236/ijmnta.2013.22018                

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).

Keywords

Bernstein Polynomial; Operational Matrix; Integro-Differential Equations

Conflicts of Interest

The authors declare no conflicts of interest.

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