Yang, Yin Jacobi spectral Galerkin methods for Volterra integral equations with weakly singular kernel. (English) Zbl 1341.65053 Bull. Korean Math. Soc. 53, No. 1, 247-262 (2016). For the weakly singular Volterra integral equation \(y(t)=\int_0^t(t-\tau)^{-\gamma}K(t,\tau)y(\tau)d\tau+f(t)\) with \(0<\gamma<1\), the author discusses a polynomial Galerkin method based on a Jacobi weight function. In addition, a fully discrete variant of this method is proposed where the integrals that arise in the construction of the method are approximately computed via a Gauss quadrature scheme with the same weight function. A few error estimates are given. These estimates require a certain degree of smoothness of the solution. This assumption may be difficult to satisfy in practical applications due to the singularity in the kernel of the integral operator. Reviewer: Kai Diethelm (Braunschweig) Cited in 12 Documents MSC: 65R20 Numerical methods for integral equations 45D05 Volterra integral equations 45E05 Integral equations with kernels of Cauchy type Keywords:spectral Galerkin methods; pseudo-spectral Galerkin method; Jacobi polynomial; weakly singular Volterra integral equation; Gauss quadrature scheme; error estimates PDFBibTeX XMLCite \textit{Y. Yang}, Bull. Korean Math. Soc. 53, No. 1, 247--262 (2016; Zbl 1341.65053) Full Text: DOI Link