The Numerical Solution of Nonlinear Volterra Integral Equations of the Second Kind by Collocation and Iterated Collocation Methods
The Numerical Solution of Nonlinear Volterra Integral Equations of the Second Kind by Collocation and Iterated Collocation Methods
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DOI：
10.1137/0908068
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发表时间：
1987-09
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影响因子：
--
通讯作者：
J. Blom;H. Brunner
中科院分区：
文献类型：
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作者：
J. Blom;H. Brunner
本文研究了求解一般非线性第二类沃尔泰拉积分方程的一种配置型变步长一步法。本文将多项式样条配点的迭代配点法推广到第二类非线性沃尔泰拉积分方程。由此产生的超收敛性能的配置近似或迭代配置近似用于获得（局部和全局）的误差估计，这反过来又形成了一个可变步长代码的基础。该代码的性能通过大量的测试问题来说明。
The subject of this paper is a variable stepsize one-step method of collocation type for solving general nonlinear second kind Volterra integral equations. We extend the iterated collocation method corresponding to polynomial spline collocation to nonlinear Volterra integral equations of the second kind. The resulting superconvergence properties of either the collocation approximation or the iterated collocation approximation are used to obtain (local and global) error estimates which in turn form the basis of a variable stepsize code. The performance of this code is illustrated by means of numerous test problems.