Smoothing transformation and piecewise polynomial collocation for Volterra integro-differential equations with weakly singular kernels

被引：0

作者：

Kolk, Marek ^{[1
]}

Pedas, Arvet ^{[1
]}

机构：

[1] Institute of Applied Mathematics, University of Tartu, Liivi Street 2, 50409 Tartu, Estonia

来源：

WSEAS Transactions on Mathematics | 2007年 / 6卷 / 04期

关键词：

Convergence of numerical methods - Mathematical transformations - Polynomials;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The numerical solution of linear weakly singular Volterra integro-differential equations is studied. Using an integral equation reformulation of the initial value problem, we apply to it a smoothing transformation so that the exact solution of the resulting equation does not contain any singularities in its derivatives up to a certain order. After that the regularized equation is solved by a piecewise polynomial collocation method on a mildly graded or uniform grid. Global convergence estimates are derived and some superconvergence results are given.

引用

页码：537 / 544

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