Numerical analysis of very weakly well-posed hyperbolic Cauchy problems
Numerical analysis of very weakly well-posed hyperbolic Cauchy problems
复制标题
极弱适定双曲柯西问题的数值分析
DOI：
10.1093/imanum/dru025
复制
发表时间：
2015
影响因子：
2.1
通讯作者：
J. Rauch
中科院分区：
文献类型：
--
作者：
F. Colombini;J. Rauch
This paper analyses the approximate solution of very weakly well-posed hyperbolic Cauchy problems. These problems have very sensitive dependence on initial data. We treat a single family of such problems showing that, in spite of the sensitive dependence, approximate solutions with desired precision ε can be computed in finite-precision arithmetic with cost growing polynomially in 1/ε. The sensitive dependence requires high finite precision. The analysis required a new Gevrey stability estimate for the leapfrog scheme. The latter depends on a new discrete Glaeser inequality. The cost of calculating solutions with features on a scale ℓ≪1 grows as eCℓ−1/2.
