Numerical Calculations Using Maple: Why & How?
E. V. Correa Silva, L. G. S. Duarte, L. A. C. P. da Mota, J. E. F. Skea
TL;DR
This paper addresses the challenge of integrating Maple with high-performance numeric languages to perform extensive numerical calculations for chaotic dynamical systems. It presents Ndynamics, a Maple-based environment that coordinates symbolic problem setup with compiled numeric kernels via the system command and black-box interfaces, exemplified by a Runge-Kutta 5th-order method. The work shows how to compute trajectories and detect chaotic regions, estimate fractal dimensions such as the Hausdorff dimension $d$ and boundary dimension $d_B$ using Boxcount and Fdimension, and compares performance against pure Maple numerics. It discusses design principles for hybrid symbolic-numeric software—including data exchange, plug-and-play numerics, and the use of black-box components—and outlines a roadmap for user-supplied numerical code. Overall, the Ndynamics framework demonstrates a practical, scalable approach to combining Maple's interactivity with fast numeric kernels for nonlinear dynamics.
Abstract
The possibility of interaction between Maple and numeric compiled languages in performing extensive numeric calculations is exemplified by the Ndynamics package, a tool for studying the (chaotic) behavior of dynamical systems. Programming hints concerning the construction of Ndynamics are presented. The system command, together with the application of the black-box concept, is used to implement a powerful cooperation between Maple code and some other numeric language code.