A Legendre-Gauss collocation method for neutral functional-differential equations with proportional delays

作者：Bhrawy Ali H^*; Assas Laila M; Tohidi Emran; Alghamdi Mohammed A

来源：Advances in Difference Equations, 2013, 63.

DOI：10.1186/1687-1847-2013-63

• delay differential equations
• neutral functional-differential equations
• proportional delays
• spectral method
• Legendre-Gauss quadrature

In this paper, we present a unified framework for analyzing the spectral collocation method for neutral functional-differential equations with proportional delays using shifted Legendre polynomials. The proposed collocation technique is based on shifted Legendre-Gauss quadrature nodes as collocation knots. Error analysis and stability of the proposed algorithm are theoretically investigated under several mild conditions. The accuracy of the proposed method has been compared with a variational iteration method, a one-leg theta-method, a particular Runge-Kutta method, and a reproducing kernel Hilbert space method. Numerical results show that the proposed methods are of high accuracy and are efficient for solving such an equation. Also, the results demonstrate that the proposed method is a powerful algorithm for solving other delay differential equations.

• 出版日期2013-3-20