Spectral collocation methods for Volterra-integro differential equations with noncompact kernels

The aim of this paper is to analyze spectral collocation methods for a class of Volterra-integro differential equations with noncompact kernels. The spectral collocation method is proposed to solve the equations after the results on existence, uniqueness and regularity of the solutions are established. The convergence rates of the methods are proven and a numerical example is provided to verify the theoretical findings.