The three-body problem, which describes three masses interacting through Newtonian
gravity without any restrictions imposed on the initial positions and velocities of these …

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Since the creation of the digital computer, numerical computations have played an
increasingly fundamental role in modeling physical phenomena for science and …

Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous
Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the …

This study shows how to obtain least-squares solutions to initial value problems (IVPs),
boundary value problems (BVPs), and multi-value problems (MVPs) for nonhomogeneous …

This paper revisits the use of the Taylor series method for the numerical integration of ODEs
and DAEs. The numerical method is implemented using an efficient variable-step variable …

Consider a continuous dynamical system for which partial information about its current state
is observed at a sequence of discrete times. Discrete data assimilation inserts these …

This work arises from the purpose of applying new tools in dynamical systems to time
problems in biological systems. The main aim of this paper is to develop a numerical method …

At the intersection between computer science and astrodynamics lies a fertile ground for
improving methodologies and performances of spacecraft trajectory computations. In this …

This article introduces the software package TIDES and revisits the use of the Taylor series
method for the numerical integration of ODEs. The package TIDES provides an easy-to-use …