Some recent advances in validated methods for IVPs for ODEs

By K. Jackson, Nedialko S. Nedialkov. 2002

60 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/1644760d809ed13e2df97d6f95205003764b1a69

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Jinglai Wu
2. Zhen Luo
3. Youdong Lin
4. Mark A. Stadtherr
5. Yunqing Zhang
6. Nong Zhang
7. Liping Chen
8. Nedialko S. Nedialkov

In Statistical and Nonlinear Physics

1. Youdong Lin
2. Mark A. Stadtherr
3. Zhen Luo
4. Jinglai Wu
5. Yunqing Zhang
6. Nong Zhang
7. Liping Chen
8. J. Pryce

In Signal Processing

1. Youdong Lin
2. Mark A. Stadtherr
3. Zhen Luo
4. Jinglai Wu
5. Yunqing Zhang
6. Liping Chen
7. Nong Zhang

Citations in the corpus

• Solving Differential-Algebraic Equations by Taylor Series (I): Computing Taylor Coefficients (2005, background): “They are also the basis of current validated ODE solvers, which produce rigorous bounds on the numerical solution [ 16 , 23, 24].”
• Validated solutions of initial value problems for parametric ODEs (2007, methodology): “Nedialkov’s VNODE package employs QR together with an interval Hermite-Obreschko method [ 27 , 29], which can be viewed as a type of generalized Taylor method, and improves on AWA.”
• Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions (2013, methodology): “To this end, many other schemes are required to be incorporated into the interval method to control the overestimation, such as the Interval Taylor series method [20, 25] and Taylor model method [26].”