The h-p-version of spline approximation methods for Mellin convolution equations.

We consider the numerical solution of Mellin convolution equations on an interval by the h-p-version of spline approximation methods. Using a geometric mesh refinement towards the singularity of the integral equation, we prove stability and exponential convergence in the Lq norm, 1 ≤ q ≤ ∞, for Galerkin, collocation and Nyström methods based on piecewise polynomials