Optimal prediction of stiff oscillatory mechanics.
نویسنده
چکیده
We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations that are easier to solve numerically. We demonstrate by examples that optimal prediction can reduce the amount of computation needed to obtain a solution by several orders of magnitude.
منابع مشابه
On second derivative 3-stage Hermite--Birkhoff--Obrechkoff methods for stiff ODEs: A-stable up to order 10 with variable stepsize
Variable-step (VS) second derivative $k$-step $3$-stage Hermite--Birkhoff--Obrechkoff (HBO) methods of order $p=(k+3)$, denoted by HBO$(p)$ are constructed as a combination of linear $k$-step methods of order $(p-2)$ and a second derivative two-step diagonally implicit $3$-stage Hermite--Birkhoff method of order 5 (DIHB5) for solving stiff ordinary differential equations. The main reason for co...
متن کاملA hybrid method with optimal stability properties for the numerical solution of stiff differential systems
In this paper, we consider the construction of a new class of numerical methods based on the backward differentiation formulas (BDFs) that be equipped by including two off--step points. We represent these methods from general linear methods (GLMs) point of view which provides an easy process to improve their stability properties and implementation in a variable stepsize mode. These superioritie...
متن کاملAn Averaging Technique for Highly Oscillatory Hamiltonian Problems
In this paper, we are concerned with the numerical solution of highly-oscillatory Hamiltonian systems with a stiff linear part. We construct an averaged system whose solution remains close to the exact one over bounded time intervals, possesses the same adiabatic and Hamiltonian invariants as the original system, and is non-stiff. We then investigate its numerical approximation through a method...
متن کاملOscillatory MHD Flow of Blood through an Artery with Mild Stenosis (RESEARCH NOTE)
The purpose of this work is to study the effect of oscillatory MHD blood flow in stenosed artery. The analytical and numerical results are obtained for oscillatory MHD blood flow, which is assumed to be a Newtonian fluid. It was also assumed that the surface roughness is of cosine shaped and the maximum height of roughness is negligible, compared with the radius of un-constricted tube. The flui...
متن کاملHigh-frequency oscillatory ventilation in neonatal RDS: initial volume optimization and respiratory mechanics.
To determine whether initial lung volume optimization influences respiratory mechanics, which could indicate the achievement of optimal volume, we studied 17 premature infants with respiratory distress syndrome (RDS) assisted by high-frequency oscillatory ventilation. The continuous distending pressure (CDP) was increased stepwise from 6-8 cmH2O up to optimal CDP (OCDP), i.e., that allowing goo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 97 12 شماره
صفحات -
تاریخ انتشار 2000