Validated solutions of initial value problems for ordinary differential equations
Validated solutions of initial value problems for ordinary differential equations
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DOI：
10.1016/s0096-3003(98)10083-8
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发表时间：
1999-10
期刊：
影响因子：
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通讯作者：
N. Nedialkov;K. Jackson;G. Corliss
中科院分区：
文献类型：
--
作者：
N. Nedialkov;K. Jackson;G. Corliss
与常微分方程组初值问题的标准数值方法相比，求解常微分方程组初值问题的有效方法有两个重要的优点：如果返回问题的解，则(1)保证问题有唯一解；(2)产生真解的封闭性。作者综述了用于常微分方程组IVP有效解的泰勒级数方法，在一个公共框架中描述了几种这样的方法，并确定了未来研究的领域。
Compared to standard numerical methods for initial-value problems (IVPs) for ordinary differential equations (ODEs), validated methods for IVPs for ODEs have two important advantages: if they return a solution to a problem, then (1) the problem is guaranteed to have a unique solution, and (2) an enclosure of the true solution is produced. The authors survey Taylor series methods for validated solutions of IVPs for ODEs, describe several such methods in a common framework, and identify areas for future research.