Theoretical analysis of Sinc-Nyström methods for Volterra integral equations

Tomoaki Okayama, Takayasu Matsuo, Masaaki Sugihara
2014 Mathematics of Computation  
In this paper, we present three theoretical results on Sinc-Nyström methods for Volterra integral equations of the first and second kind, which were proposed by Muhammad et al. Their methods involve the following issues: 1) it is difficult to determine the tuning parameter unless the solution is given, and 2) convergence has not been proved in a precise sense. In a mathematically rigorous manner, we present an implementable way to estimate the tuning parameter and a rigorous proof of the
more » ... proof of the convergence with its rate explicitly revealed. Furthermore, we show that the resulting system is well conditioned. Numerical examples that support the theoretical results are also presented.
doi:10.1090/s0025-5718-2014-02929-3 fatcat:3zabiski7jh5nk4bbogxq7r6uu