PHASER: A Universal Simulator for Dynamical Systems

在过去的二十年中，微分方程及其应用的本科课程通过采用数值模拟和科学可视化发生了革命性的变化。一些著名的商业软件产品，包括1989年获得EDUCOM/NCRIPTAL“高等教育最佳数学软件”奖的Phaser，使这场革命成为可能。最初的Phaser已经完全用Java重写，Java是一种平台中立的语言，具有出色的Internet支持。添加了许多新的可视化特性，特别是用于查看和组织多个模拟的Gallery。该项目支持Phaser的三项全面开发活动：(a)开发和免费分发Phaser的浏览器版本，类似于Adobe的AcrobatReader；并促进动态相位器项目和画廊在互联网上的广泛分布。(b)与数学家、科学家和工程师合作，建立一个多学科微分和差分方程项目门户网站，将这些项目发布在www.phaser.com上，并创建适合本科生和高级本科生的动力系统及其应用画廊。(c)与不同机构的学生和教师一起测试和评价相位器的使用。此外，Phaser数值引擎的开发仍在继续。正在开发和测试方法，以验证使用阴影概念的混沌系统的数值模拟。

In past two decades, undergraduate courses in differential equations and their applications have undergone revolutionary changes by embracing numerical simulations and scientific visualization. Several notable commercial software products, including Phaser, the winner of EDUCOM/NCRIPTAL "Best Mathematics Software in Higher Education" award in 1989, have made this revolution possible. The original Phaser has been completely rewritten in Java, a platform-neutral language with excellent Internet support. Many new visualization features have been added, notably a Gallery for viewing and organizing multiple simulations. This project is supporting three full-scale development activities for Phaser:(a) Developing and distributing freely a browser version of Phaser, akin to AcrobatReader by Adobe; and facilitating wide distribution of dynamic Phaser Projects and Galleries over the Internet.(b) Creating a portal of multidisciplinary differential and difference equationsprojects in collaboration with mathematicians, scientists, and engineers, posting these projects on www.phaser.com, and creating Galleries for dynamical systems and their applications suitable for beginning and advanced undergraduate students.(c) Testing and evaluating the use of Phaser with students and faculty at diverse institutions.In addition, development continues on the Phaser numerical engine. Methods are being developed and tested for validating numerical simulations of chaotic systems using the concept of shadowing.