Jacobi-spectral method for integro-delay differential equations with weakly singular kernels

Authors : İshtiaq ALI

Pages : 810-819

View : 10 | Download : 8

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :We present a numerical solution to the integro-delay differential equation with weakly singular kernels with the delay function $\theta insert ignore into journalissuearticles values(t);$ vanishing at the initial point of the given interval $[0, T]$ insert ignore into journalissuearticles values($\theta insert ignore into journalissuearticles values(t); = qt, 0 < q < 1);$. In order to fully use the Jacobi orthogonal polynomial theory, we use some function and variable transformation to change the intergro-delay differential equation into a new equation defined on the standard interval $[-1, 1]$. A Gauss--Jacobi quadrature formula is used to evaluate the integral term. The spectral rate of convergence is provided in infinity norm under the assumption that the solution of the given equation is sufficiently smooth. For validation of the theoretical exponential rate of convergence of our method, we provide some numerical examples.
Keywords : Jacobi spectral methods, integro delay differential, weakly singular kernels equations, Gauss Jacobi quadrature formula, numerical examples