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Turkish Journal of Mathematics

Authors

ISHTIAQ ALI

DOI

10.3906/mat-1409-67

Abstract

We present a numerical solution to the integro-delay differential equation with weakly singular kernels with the delay function $\theta (t)$ vanishing at the initial point of the given interval $[0, T]$ ($\theta (t) = qt, 0 < q < 1)$. 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.

First Page

810

Last Page

819

Included in

Mathematics Commons

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