Turkish Journal of Mathematics
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.
Keywords
Jacobi spectral methods, integro-delay differential, weakly singular kernels equations, Gauss--Jacobi quadrature formula, numerical examples
First Page
810
Last Page
819
Recommended Citation
ALI, ISHTIAQ
(2015)
"Jacobi-spectral method for integro-delay differential equations with weakly singular kernels,"
Turkish Journal of Mathematics: Vol. 39:
No.
6, Article 2.
https://doi.org/10.3906/mat-1409-67
Available at:
https://journals.tubitak.gov.tr/math/vol39/iss6/2
