  We propose a spectral collocation method, based on the generalized Jacobi
wavelets along with the Gauss-Jacobi quadrature formula, for solving a class of
third-kind Volterra integral equations. To do this, the interval of integration
is first transformed into the interval [-1,1], by considering a suitable change
of variable. Then, by introducing special Jacobi parameters, the integral part
is approximated using the Gauss-Jacobi quadrature rule. An approximation of the
unknown function is considered in terms of Jacobi wavelets functions with
unknown coefficients, which must be determined. By substituting this
approximation into the equation, and collocating the resulting equation at a
set of collocation points, a system of linear algebraic equations is obtained.
Then, we suggest a method to determine the number of basis functions necessary
to attain a certain precision. Finally, some examples are included to
illustrate the applicability, efficiency, and accuracy of the new scheme.
