Asymptotic error analysis of the Adaptive Verlet method

被引：12

作者：

Cirilli, S

Hairer, E

Leimkuhler, B

机构：

[1] Univ Geneva, Sect Math, CH-1211 Geneva 24, Switzerland

[2] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

来源：

BIT NUMERICAL MATHEMATICS | 1999年 / 39卷 / 01期

基金：

美国国家科学基金会;

关键词：

Adaptive Verlet method; time-reversible variable stepsizes; Hamiltonian systems; Sundman time-transformations; backward error analysis; asymptotic expansions;

D O I：

10.1023/A:1022313123291

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

The Adaptive Verlet method and variants are time-reversible schemes for treating Hamiltonian systems subject to a Sundman time transformation. These methods have been observed in computer experiments to exhibit superior numerical stability when implemented in a counterintuitive "reciprocal" formulation. Here we give a theoretical explanation of this behavior by examining the leading terms of the modified equation (backward error analysis) and those of the asymptotic error expansion. With this insight we are able to improve the algorithm by simply correcting the starting stepsize. AMS subject classification: 65L06, 65L20.

引用

页码：25 / 33

页数：9

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