A multi-domain spectral collocation method for Volterra integral equations with a weakly singular kernel

In this paper, we introduce a multi-domain Muntz-polynomial spectral collocation method with graded meshes for solving second kind Volterra integral equations with a weakly singular kernel. This method is particularly suitable for problems whose solutions contain non-integer exponent factors. We carry out a rigorous error analysis of hp-version in the L ∞ - and weighted L 2 -norms. Several numerical examples are presented to demonstrate the efficiency and accuracy of the method.