任意阶微分代数方法的面向对象编程实现  

Object Oriented Implementation of Differential Algebraic Method with Arbitrary High Order

作　　者：王莉萍[1] 唐天同[1] 程彬杰[1] 蔡杰[1] 

机构地区：[1]西安交通大学,西安710049

出　　处：《西安交通大学学报》2000年第6期54-58,共5页Journal of Xi'an Jiaotong University

摘　　要：为给研究非线性系统传递性质提供一个简便、有效的工具 ,研究了新近出现的微分代数的基本理论 ,在VC ++环境中编制了一个DA/TLC软件包 ,实现了任意高阶微分代数的功能 .通过一些例子对此软件进行了计算测试 ,其结果与解析解完全一致 ,这为任意高阶微分的计算提供了一种可达到机器精度的极为简便的数值工具 ,可用于非线性系统任意阶传递性质的分析计算 .Differential algebra provides a new and promising mathematical method based on the nonstandard analysis and power series theory.The underlying principle is studied for calculating the transfer properties of nonlinear systems. Using the object oriented programming technique and Visual C++ ,a DA/TLC package was developed, and it could implemen differential algebra up to arbitrary high order. The package was tested and the results agree well with the analytic solutions. The present work presents a straightforward and effective tool for computing arbitrary order derivatives with accuracy up to the precision of computers. It is of importance for studying nonlinear transfer properties up to arbitrary order.

关 键 词：微分代数 面向对象编程 非线性微分方程 软件包 

分 类 号：O241.4[理学—计算数学] O241.81[理学—数学]