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.