A dynamic model is a model that describes how a system changes in time. In some cases, time is the only independent variable, and in others, there are additional variables such as those of spatial frames. Even though the concept of creating a dynamic model, capturing the dynamics of a system, is ubiquitous, the topic tends to be splintered across numerous disciplines, from mathematical modeling and computer simulation to more qualitative models for software design and science. Moreover, models have a variety of representations from the traditional notations of mathematics to diagrammatic, and even immersive representations. The purpose of this volume is to provide a text that brings together all of these expressions for dynamic models.
The emphasis in the Handbook on Dynamical Systems Modeling is on presenting a “computer science slant” toward the problems of model design, representation, and analysis. As such, each chapter will be of a tutorial or survey nature, including mathematical descriptions, pseudocode, and diagrams wherever possible. The idea is to inform the reader as to how to use the model(s). (Paul Fishwick 2006)
Although differential equations can be solved using almost any programming language, we have chosen Java to illustrate particular algorithmic implementations. Java is an object-oriented programming language that is designed to run on a virtual computer that can be implemented for any modern operating system. This promise of platform independence has become a reality, and we now can write programs that have attractive graphical user interfaces and support common tasks such as printing, disk access, and copy-paste data exchange with other applications. Readers who are unfamiliar with or uninterested in Java may treat the code listing as pseudocode while Java programmers can compile and run the examples.
Ordinary Differential Equations
Please send comments/corrections to Wolfgang Christian or Francisco Esquembre.
You are encouraged to download the following jar file to execute examples of how we use the Opens Source Physics code library to solve systems of first order ordinary differential equations.
| Archive | Description |
|---|---|
| osp_ode_examples.jar | Examples of how to use the OSP library to solve ordinary differential equations. |
Examples from other areas of physics and mathematics are available in the Applets and Applications Section of this website.
You may directly access (browse) the binary directory on this website for additional OSP jar files but please note that this binary directory also contains code libraries (jar files) that are not designed to run as stand-alone applications.
Source code for the pendulum, the chemical reaction, the predator-prey, and the planetary motion examples as well as the OSP library are available on the Open Source Physics developer website.
An alternative approach to the solving ordinary differential equations is to use a high-level modeling program. The Easy Java Simulations (Ejs) authoring tool provides a simple way to create simulations for continuous (and noncontinuous) systems, together with easy-to-use graphical elements to visualize the state of the system and its evolution. The Ejs graphical user interface enables users to build simulations using a model-control-view paradigm. These simulations can then be used to explore the behavior of the system under different conditions. You are encouraged to download the following jar file to execute these examples.
| Archive | Description |
|---|---|
| ejs_crcExamples.jar | Easy Java Simulations (Ejs) demonstrations. Each demonstration was created with the Ejs modeling program. Multiple demonstrations are combined in this jar file as a Launcher package. |
Additional Ejs simulations (including the the Ejs modeling tool) can be found at: