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

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DOI: 10.4236/am.2014.515228    4,456 Downloads   4,990 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Khader, M. , Mahdy, A. and Shehata, M. (2014) An Integral Collocation Approach Based on Legendre Polynomials for Solving Riccati, Logistic and Delay Differential Equations. Applied Mathematics, 5, 2360-2369. doi: 10.4236/am.2014.515228.

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