Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes

Author: Hermann Brunner
Journal: Math. Comp. 45 (1985), 417-437
MSC: Primary 65R20; Secondary 45D05
MathSciNet review: 804933
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Since the solution of a second-kind Volterra integral equation with weakly singular kernel has, in general, unbounded derivatives at the left endpoint of the interval of integration, its numerical solution by polynomial spline collocation on uniform meshes will lead to poor convergence rates. In this paper we investigate the convergence rates with respect to graded meshes, and we discuss the problem of how to select the quadrature formulas to obtain the fully discretized collocation equation.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65R20, 45D05

Retrieve articles in all journals with MSC: 65R20, 45D05

Additional Information

Keywords: Volterra integral equations, weakly singular kernels, polynomial spline collocation, graded meshes
Article copyright: © Copyright 1985 American Mathematical Society