About ODE Architect

ODE Architect is a Windows software package that provides a highly interactive software environment for constructing and exploring your own ODE models of real-world phenomena. It is bundled with some popular differential equations textbooks or can be purchased by itself.

Components

ODE Architect has three components: the ODE Architect Tool,  the Multimedia ODE Architect, and the ODE Architect Library.  ODE Architect (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 L. F. Shampine and I. Gladwell. 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 CODEE-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 variety of 2D and 3D graphics. A second mode of operation, the Expert Mode, provides access to more advanced features.

The robust Tool solves 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 and used. 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 one 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 Architect Library

The ODEA Library has dozens of pre-programmed, 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 with descriptive titles to facilitate browsing. These files also provide a marvelous way to learn how to use the Architect Tool.

Documentation

Click here to see the Guide to the ODE Architect Tool, written by Michael Moody.

Award

ODE Architect  was named one of “The Nine Best Digital Projects on the Planet” by NewMedia magazine in its December, 1998, issue. ODE Architect was one of 1,080 entries in 40 categories submitted to the New Media INVISION '98 Awards and one of only nine given an Award of Excellence. ODE Architect also won a gold medal in the category of Higher Education. A NSF/DUE grant to CODEE made it possible to produce ODE Architect with support from John Wiley & Sons, and Intellipro, Inc.