ISSN:
1572-9125
Keywords:
Adaptive Verlet method
;
time-reversible variable stepsizes
;
Hamiltonian systems
;
Sundman time-transformations
;
backward error analysis
;
asymptotic expansions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1022313123291
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