Polynomial Collocation Methods Based On Successive Integration Technique For Solving System Of Neutral Delay Differential Equations
DOI:
https://doi.org/10.23755/rm.v48i0.1417Keywords:
Polynomials, Collocation method, Successive Integration Technique, Neutral Delay Differential Equations.Abstract
This paper presents a new approach to using polynomials such as Hermite, Bernoulli,
Chebyshev, Fibonacci and Bessel to solve a system of linear and nonlinear neutral delay
differential equations. The proposed method is based on the truncated polynomial
expansion of the function together with collocation points and successive integration
techniques. This method reduces the given equation to system of non-linear equations
with unknown polynomial coefficients which can be easily calculated. The convergence
of the proposed method is discussed with several mild conditions. Numerical examples
are considered to demonstrate the efficiency of the method. The numerical results reveal
that the proposed new approach gives better results than other conventional methods. It
demonstrates the reliability and efficiency of this method for solving a system of linear
and nonlinear neutral delay differential equations.
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