Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

On the Extension of Adams–Bashforth–Moulton Methods for Numerical Integration of Delay Differential Equations and Application to the Moon’s Orbit

On the Extension of Adams–Bashforth–Moulton Methods for Numerical Integration of Delay... One of the problems arising in modern celestial mechanics is the need of precise numerical integration of dynamical equations of motion of the Moon. The action of tidal forces is modeled with a time delay and the motion of the Moon is therefore described by a functional differential equation (FDE) called delay differential equation (DDE). Numerical integration of the orbit is normally being performed in both directions (forwards and backwards in time) starting from some epoch (moment in time). While the theory of normal forwards-in-time numerical integration of DDEs is developed and well-known, integrating a DDE backwards in time is equivalent to solving a different kind of FDE called advanced differential equation, where the derivative of the function depends on not yet known future states of the function. We examine a modification of Adams–Bashforth–Moulton method allowing to perform integration of the Moon’s DDE forwards and backwards in time and the results of such integration. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematics in Computer Science Springer Journals

On the Extension of Adams–Bashforth–Moulton Methods for Numerical Integration of Delay Differential Equations and Application to the Moon’s Orbit

Mathematics in Computer Science , Volume 14 (1) – Mar 14, 2020

Loading next page...
 
/lp/springer-journals/on-the-extension-of-adams-bashforth-moulton-methods-for-numerical-VrR0oCTbUn

References (17)

Publisher
Springer Journals
Copyright
Copyright © Springer Nature Switzerland AG 2020
ISSN
1661-8270
eISSN
1661-8289
DOI
10.1007/s11786-019-00447-y
Publisher site
See Article on Publisher Site

Abstract

One of the problems arising in modern celestial mechanics is the need of precise numerical integration of dynamical equations of motion of the Moon. The action of tidal forces is modeled with a time delay and the motion of the Moon is therefore described by a functional differential equation (FDE) called delay differential equation (DDE). Numerical integration of the orbit is normally being performed in both directions (forwards and backwards in time) starting from some epoch (moment in time). While the theory of normal forwards-in-time numerical integration of DDEs is developed and well-known, integrating a DDE backwards in time is equivalent to solving a different kind of FDE called advanced differential equation, where the derivative of the function depends on not yet known future states of the function. We examine a modification of Adams–Bashforth–Moulton method allowing to perform integration of the Moon’s DDE forwards and backwards in time and the results of such integration.

Journal

Mathematics in Computer ScienceSpringer Journals

Published: Mar 14, 2020

There are no references for this article.