ODE Architect

ODE Architect (ODEA) is a Windows software package that provides a highly interactive software environment for constructing and exploring your own ODE models of real-world phenomena, no matter whether they lead to linear or nonlinear systems. ODEA is sold by John Wiley & Sons on CD-ROM with an accompanying book. (It can be purchased from a variety of retailers

Note that versions 1.6 and below of ODE Architect will not run on Windows Vista or Windows 7. You must have Windows XP (or a previous version) to run ODE Architect at this time. Complaints and requests for support should be directed to Wiley.

The free, cross-platform Java application, ODE Toolkit provides some, but not all, of the functionality of ODE Architect.

Components

There are three components in the ODEA package: the ODE Architect Tool, the Multimedia ODE Architect, and the ODE Library.

ODEA was designed to be easy to use. Navigational paths are clearly marked and simple to follow using a point-and-click technique. At any place in the package you will be able to call up content menus and access material in any order.

The ODE Architect Tool

The ODE Architect Tool is a first-rate, research-quality numerical ODE solver and graphics package. The solvers are based on those developed by Profs. L. F. Shampine and I. Gladwell of Southern Methodist University. For a delightfully readable account on using numerical solvers in teaching ODEs, see their paper,

Shampine, L. F., and Gladwell, I., “Teaching Numerical Methods in ODE Courses” in the C*ODE*E-inspired book Revolutions in Differential Equations, edited by Michael Kallaher, MAA Notes # 50.

The Tool employs a graphical user interface to enter and edit equations, control solver settings and features, and to create and edit a wide vartiety of 2D and 3D graphics. A second mode of operation, the Expert Mode, provides access to more advanced features.

The robust Tool will solve systems of up to ten first-order ODEs which can be entered using a simple, natural scripting language. Auxiliary functions involving the state variables can be defined. A solver/grapher feature for discrete dynamical systems is also available from the Tool.

A variety of engineering functions such as square waves, sawtooth waves and step functions are included in the Tool function library. Time and parameter animations of solution data are supported. Initial conditions for planar systems can be entered by clicking in a graph window or via the keyboard. Graph scales can be set automatically or manually. Numerical values of solutions can be viewed in tabular form. Parameter-sensitive analysis is made easy with a built-in parameter sweep tool.

Graphs are editable and you can scale and label axes, mark equidistant-in-time orbital points, color the graphs, change the line styles, overlay graphs of functions and solution curves for different ODEs—all with no programming or special commands to remember

Multimedia ODE Architect

Multimedia ODE Architect illustrates the modeling process in detail, with dozens of examples, each with its own theme, supported by highly interactive simulations. Students explore the modeling process via “what-if” scenarios and exercises. Along the way, students are guided to build their own ODEs which model a given situation and then solve them numerically and graphically.

The ODE Library

The ODE Library has dozens of preprogrammed, editable, and interactive ODE files covering a wide range of topics from mathematics, physics, chemistry, population biology, and epidemiology. There are also many ODEs to illustrate points such as data compression, ODEs with singular coefficients, bifurcation, limit cycles, and so on. Each Library file has explanatory text along with the ODEs and include illustrative graphs. The Library files are organized into folders and they have descriptive titles to facilitate browsing. These files also provide a marvelous way to learn how to use the Architect Tool.