Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind
The authors extend the known method of collocations to approximate solving a Volterra integral equation with the singular kernel \[ y(t) = g(t)+ \int_{0}^{t} (t-s)^{\mu} K(t,s)y(s)ds \] for the case \(\mu =1/2\). The convergence of this method is proved using the quadrature formulas defined by Jacobi polynomials, but for numerical experiments only the Lagrangian polynomials are used.
Abel-Volterra singular integral equation
scientific article; zbMATH DE number 6107738
scientific article