Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1705-87
Keywords
Fully discretized multiprojection method, collocation method, weakly singular Volterra integral equations, local convergence, error analysis
First Page
1400
Last Page
1423
Recommended Citation
BEYRAMI, H, & LOTFI, T (2018). On the local superconvergence of the fully discretized multiprojection method for weakly singular Volterra integral equations of the second kind. Turkish Journal of Mathematics 42 (3): 1400-1423. https://doi.org/10.3906/mat-1705-87
