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K. Maleknejad, E. Hashemizadeh and B. Basirat, “Computational Method Based on Bernestein Operational Matrices for Nonlinear Volterra—Fredholm-Hammerstein Integral Equations,” Communications in Nonlinear Science and Numerical Simulation, Vol. 17, No. 1, 2012, pp. 52-61. doi:10.1016/j.cnsns.2011.04.023

has been cited by the following article:

• 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).