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摘要
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 epsilon can be computed in finite-precision arithmetic with cost growing polynomially in 1/epsilon. 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 e(cl-1/2).
- 出版日期2015-7
