An hp-version fractional collocation method for Volterra integro-differential equations with weakly singular kernels.

In this paper, we propose an hp -version fractional collocation method for solving second kind Volterra integro-differential equations with weakly singular kernels. We derive hp -version error estimates in a weighted H 1 -norm for the method on arbitrary meshes. The results show that for any given mesh partition, exponential rates of convergence can be achieved for certain weakly singular solutions by linearly increasing the degrees of piecewise fractional polynomials. The results also imply that in the case of uniform mesh, the method has no ( h -version) order barrier for weakly singular solutions, which is different from classical polynomial collocation methods. The method is easy to implement and has the same computational complexity as polynomial collocation methods. Numerical experiments are presented to demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]