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Sweilam, N.H., Khader, M.M. and Mahdy, A.M.S. (2013) Numerical Study for the Fractional Differential Equations Generated by Optimization Problem Using Chebyshev Collocation Method and FDM. Applied Mathematics and Information Science, 7, 2013-2020.

has been cited by the following article:

• TITLE: An Integral Collocation Approach Based on Legendre Polynomials for Solving Riccati, Logistic and Delay Differential Equations

  AUTHORS: M. M. Khader, A. M. S. Mahdy, M. M. Shehata

  KEYWORDS: Integral Collocation Formulation, Spectral Method, Riccati, Logistic and Delay Differential Equations

  JOURNAL NAME: Applied Mathematics, Vol.5 No.15, August 19, 2014

  ABSTRACT: In this paper, we propose and analyze some schemes of the integral collocation formulation based on Legendre polynomials. We implement these formulae to solve numerically Riccati, Logistic and delay differential equations with variable coefficients. The properties of the Legendre polynomials are used to reduce the proposed problems to the solution of non-linear system of algebraic equations using Newton iteration method. We give numerical results to satisfy the accuracy and the applicability of the proposed schemes.