Order of Convergence of One-Step Methods for Volterra Integral Equations of the Second Kind
Order of Convergence of One-Step Methods for Volterra Integral Equations of the Second Kind
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DOI：
10.1137/0720037
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发表时间：
1983-06
影响因子：
2.9
通讯作者：
E. Hairer;C. Lubich;S. P. Nørsett
中科院分区：
文献类型：
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作者：
E. Hairer;C. Lubich;S. P. Nørsett
对于常微分方程的一步法，收敛性和渐近展开式的良好证明是众所周知的。结果表明，这些证明可以自然地推广到第二类 Volterra 积分方程的“扩展”一步法。此外，还研究了“混合”一步法的收敛性。对于这两种类型，通用 Volterra-Runge-Kutta 方法均被视为示例。
Nice proofs of convergence and asymptotic expansions are known for one-step methods for ordinary differential equations. It is shown that these proofs can be generalized in a natural way to “extended” one-step methods for Volterra integral equations of the second kind. Furthermore, the convergence of “mixed” one-step methods is investigated. For both types general Volterra–Runge–Kutta methods are considered as examples.