TITLE:
Numerical Solution of Nonlinear Integro-Differential Equations with Initial Conditions by Bernstein Operational Matrix of Derivative
AUTHORS:
Behrooz Basirat, Mohammad Amin Shahdadi
KEYWORDS:
Bernstein Polynomial; Operational Matrix; Integro-Differential Equations
JOURNAL NAME:
International Journal of Modern Nonlinear Theory and Application,
Vol.2 No.2,
June
20,
2013
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).