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Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel. (English) Zbl 1207.65157
The authors consider Volterra integral equations of the second kind with a weakly singular kernel of the form
$y(t) = g(t) + \int_0^t (t-s)^{-\mu} K(t,s)y(s)\,ds,\;0<\mu<1,\quad 0\leq t\leq T,$
and develop a Jacobi-collocation spectral method for the above integral equation. The main aim is to use Jacobi-collocation method to numerically solve Volterra integral equation on the interval $$[-1,1]$$. They obtain higher-order accuracy for the numerical approximation using a Jacobi spectral quadrature rule for the integral term.
Finally, numerical results are given by tables and figures. Numerical and exact solutions are compared by graphics in the $$L^{\infty}$$-norm and $$L_{w}^{\infty}$$-norm.
Reviewer: Ali Filiz (Aydin)

##### MSC:
 65R20 Numerical methods for integral equations 45D05 Volterra integral equations 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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