Convergence of spline collocation for Volterra integral equations
Convergence of spline collocation for Volterra integral equations
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DOI：
10.1016/j.apnum.2007.08.004
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发表时间：
2008-10
影响因子：
2.8
通讯作者：
R. Kangro;P. Oja
中科院分区：
文献类型：
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作者：
R. Kangro;P. Oja
逐步插值预测的估计建立。根据转移矩阵的频谱，这些估计允许获得逐点收敛的投影机的身份运营商，或在某些极限情况下，证明稳定的收敛相应的近似运营商的积分方程。利用算子方程的一般收敛性定理，得到了第二类沃尔泰拉积分方程的配置法在连续函数空间或某些次连续可微函数空间中的收敛性.最实用的样条类型的情况下的应用进行了分析。
Estimates for step-by-step interpolation projections are established. Depending on the spectrum of the transfer matrix these estimates allow to obtain the pointwise convergence of the projectors to the identity operator or, in some limit cases, to prove stable convergence of the corresponding approximate operators of integral equations. This, via general convergence theorems for operator equations, permits to get the convergence of collocation method for Volterra integral equations of the second kind in spaces of continuous or certain times continuously differentiable functions. Applications in the case of the most practical types of splines are analyzed.