用于ode和DAEs的间隔工具

12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006) Pub Date : 2006-09-01 DOI:10.1109/SCAN.2006.28

N. Nedialkov

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引用次数: 108

摘要

本文综述了常微分方程初值问题解界计算的区间方法和软件的现状。我们介绍了IVP ode的VNODE- lp求解器，它是作者的VNODE包的继承者。VNODE-LP完全使用识字编程实现。VNODE-LP工作的一个主要目标是生成一个区间求解器，这样它的正确性就可以由人类专家验证，类似于数学结果的正确性验证。我们还讨论了微分代数方程解的计算界的状态。

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Interval Tools for ODEs and DAEs

We overview the current state of interval methods and software for computing bounds on solutions in initial value problems (IVPs)for ordinary differential equations (ODEs). We introduce the VNODE-LP solver for IVP ODEs, a successor of the author's VNODE package. VNODE-LP is implemented entirely using literate programming. A major goal of the VNODE-LP work is to produce an interval solver such that its correctness can be verified by a human expert, similar to how mathematical results are certified for correctness. We also discuss the state in computing bounds on solutions in differential algebraic equations.

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12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006)

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