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.
Fully discretized multiprojection method, collocation method, weakly singular Volterra integral equations, local convergence, error analysis
BEYRAMI, HOSSEIN and LOTFI, TAHER
"On the local superconvergence of the fully discretized multiprojection method for weakly singular Volterra integral equations of the second kind,"
Turkish Journal of Mathematics: Vol. 42:
3, Article 52.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/52