On the local superconvergence of the fully discretized multiprojection method for weakly singular Volterra integral equations of the second kind

Authors: HOSSEIN BEYRAMI, TAHER LOTFI

Abstract: In this paper, we extend the well-known multiprojection method for solving the second kind of weakly singular Volterra integral equations. We apply this method based on the collocation projection and develop a fully discretized version using appropriate quadrature rules. This method has a superconvergence property that the classic collocation method lacks. Although the new approach results in a significant increase in computational cost, when performing the related matrix-matrix products in parallel the computational time can be reduced. We provide a rigorous mathematical discussion about error analysis of this method. Finally, we present some numerical examples to confirm our theoretical results.

Keywords: Fully discretized multiprojection method, collocation method, weakly singular Volterra integral equations, local convergence, error analysis

Full Text: PDF