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Basirat, B. and Shahdadi, M.A. (2013) Numerical Solution of Nonlinear Integro-Differential Equations with Initial Conditions by Bernstein Operational Matrix of Derivative. International Journal of Modern Nonlinear Theory and Application, 2, 141-149.
https://doi.org/10.4236/ijmnta.2013.22018

has been cited by the following article:

• TITLE: An Extended Numerical Method by Stancu Polynomials for Solution of Integro-Differential Equations Arising in Oscillating Magnetic Fields

  AUTHORS: Neşe İşler Acar

  KEYWORDS: Stancu Polynomials, Collocation Method, Integro-Differential Equations, Linear Equation Systems, Matrix Equations

  JOURNAL NAME: Advances in Pure Mathematics, Vol.14 No.10, October 31, 2024

  ABSTRACT: In this study, the Bernstein collocation method has been expanded to Stancu collocation method for numerical solution of the charged particle motion for certain configurations of oscillating magnetic fields modelled by a class of linear integro-differential equations. As the method has been improved, the Stancu polynomials that are generalization of the Bernstein polynomials have been used. The method has been tested on a physical problem how the method can be applied. Moreover, numerical results of the method have been compared with the numerical results of the other methods to indicate the efficiency of the method.