Polynomial Collocation Methods Based on Successive Integration Technique for Solving Neutral Delay Differential Equations

Abstract

This paper presents a new approach to using polynomials such as Hermite, Bernoulli, Chebyshev, Fibonacci, and Bessel to solve 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 a system of nonlinear 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 the conventional operational matrix approach of the polynomial collocation method. It demonstrates the reliability and efficiency of this method for solving linear and nonlinear neutral delay differential equations.