期刊
APPLIED MATHEMATICS AND COMPUTATION
卷 217, 期 20, 页码 7940-7954出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2011.02.080
关键词
Taylor series method; Automatic differentiation; High-precision integration of ODEs; Variational equations; Box propagation; Freeware software
资金
- Spanish Research project [MTM2009-10767, AYA2008-05572/ESP]
This paper discusses several examples of ordinary differential equation (ODE) applications that are difficult to solve numerically using conventional techniques, but which can be solved successfully using the Taylor series method. These results are hard to obtain using other methods such as Runge-Kutta or similar schemes; indeed, in some cases these other schemes are not able to solve such systems at all. In particular, we explore the use of the high-precision arithmetic in the Taylor series method for numerically integrating ODEs. We show how to compute the partial derivatives, how to propagate sets of initial conditions, and, finally, how to achieve the Brouwer's Law limit in the propagation of errors in longtime simulations. The TIDES software that we use for this work is freely available from a website. (C) 2011 Elsevier Inc. All rights reserved.
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