The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes
The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes
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DOI：
10.1090/s0025-5718-1985-0804933-3
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发表时间：
1985-01
影响因子：
2
通讯作者：
H. Brunner
中科院分区：
文献类型：
--
作者：
H. Brunner
具有弱奇异核的第二类沃尔泰拉积分方程的解在积分区间的左端通常具有无界导数，在均匀网格上用多项式样条配置法求解该方程的数值解会导致收敛速度变差.本文研究了梯度网格下的收敛速度，并讨论了如何选择求积公式以获得完全离散的配置方程的问题。
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.