Abstract
We study the numerical solution of Volterra integral equations of the first kind by collocation methods using piecewise polynomials of degreep. We show that when superconvergence occurs, the error in the collocation solution at the node points alternates in sign, independent from the kernel or the exact solution. Evaluation at certain points of interpolating polynomials of degreep+2 annihilates, the leading term in the asymptotic expansion of the error, thus yielding convergence of orderp+3. The derivation of the asymptotic expansion of the error for the general equation is reduced to the special case of numerical differentiation by the use of an asymptotic continuity result for the projectors associated with the collocation method under compact perturbations. We present some numerical results on the improved order of convergence forp=2 and 3.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
