High-Order Methods for Volterra Integral Equations with General Weak Singularities
High-Order Methods for Volterra Integral Equations with General Weak Singularities
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DOI：
10.1080/01630560903393154
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发表时间：
2009-12
影响因子：
1.2
通讯作者：
M. Kolk;A. Pedas;G. Vainikko
中科院分区：
文献类型：
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作者：
M. Kolk;A. Pedas;G. Vainikko
构造了求解第二类线性Volterra积分方程的分段多项式配置方法。积分方程的核可能具有弱对角奇点和边界奇点。利用适当的平滑技术和多项式样条，在温和梯度或均匀网格上得到了最优的全局收敛估计，并证明了一个局部超收敛结果。
A piecewise polynomial collocation method for solving linear Volterra integral equations of the second kind is constructed. The kernel of the integral equation may have weak diagonal and boundary singularities. Using suitable smoothing techniques and polynomial splines on mildly graded or uniform grids, optimal global convergence estimates are derived and a local superconvergence result is proven.