AF: Small: Solving Linear Differential in Terms of Special Functions

AF：小：用特殊函数求解线性微分

• 批准号: 1017880
• 负责人: Mark van Hoeij
• 金额: $ 39.61万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1017880&HistoricalAwards=false
• 关键词: AF; Small; Solving; Linear; Differential

Differential equations have numerous applications in science and engineering. In this project, new algorithms will be developed to compute exact solutions of linear differential equations. The project consists of two components, a top-down approach and a bottom-up approach. The bottom-up approach is to develop an algorithm for each particular type of solutions. In contrast, the top-down algorithms are not specific to any particular type of solution, instead, the top-down algorithms aim to reduce an equation to one that is easier to solve. This complements the bottom-up approach in several ways. By reducing to an easier equation, the top-down approach can drastically reduce the computation time it takes to solve the equation. Moreover, the top-down approach also reduces the number of algorithms need to be developed and implemented in the bottom-up approach; only equations that can not be reduced any further need to be treated.

微分方程在科学和工程中有许多应用。在这个项目中，将开发新的算法来计算线性微分方程的精确解。 该项目由两个部分组成，即自上而下的方法和自下而上的方法。 自下而上的方法是为每种特定类型的解决方案开发一个算法。 相比之下，自顶向下算法并不特定于任何特定类型的解决方案，相反，自顶向下算法旨在将方程简化为更容易求解的方程。 这在几个方面补充了自下而上的方法。 通过简化为一个更简单的方程，自顶向下的方法可以大大减少求解方程所需的计算时间。 此外，自上而下的方法还减少了自下而上方法中需要开发和实现的算法的数量;仅需要处理不能进一步减少的方程。