Spline collocation method for integro-differential equations with weakly singular kernels

[摘要] In the first part of this paper we study the regularity properties of solutions to initial or boundary-value problems of Fredholm integro-clifferential equations with weakly singular or other nonsmooth kernels. We then use these results in the analysis of a piecewise polynomial collocation method for solving such problems numerically. Presented numerical examples display that theoretical results are in good accordance with actual convergence rates of proposed algorithms. (c) 2006 Elsevier B.V. All rights reserved.

[发布日期] 2006-12-01

[关键词] weakly singular integro-differential equation;piecewise polynomial collocation method;graded grid