Closed Form Solutions for Linear Differential and Difference Equations

线性微分方程和差分方程的闭式解

• 批准号: 0728853
• 负责人: Mark van Hoeij
• 金额: $ 27.5万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0728853&HistoricalAwards=false
• 关键词: Closed; Form; Solutions; Linear; Differential

Linear differential equations and difference equations appear in a wide variety of problems in mathematics and its applications. The main goal of this research is to develop a complete algorithm that finds all closed form solutions of such equations. Closed form solutions are not approximations of solutions, instead, they are given by an exact formula, written in terms of well known special functions.This research will combine a wide variety of techniques in novel ways.Key information about closed form solutions will be obtained from local data (the asymptotic behavior at each singular point) in a new way that involves interesting number theoretical and combinatorial problems. The most important feature of this new approach is that it will lead to a provably complete algorithm to find all closed form solutions.

线性微分方程和差方程出现在数学及其应用中的各种问题中。这项研究的主要目标是开发一种完整的算法，该算法找到了此类方程式的所有封闭形式解决方案。 封闭形式的解决方案不是解决方案的近似，而是由精确的公式给出，以众所周知的特殊功能为单位编写。这项研究将以新颖的方式结合各种技术。有关封闭形式解决方案的关键信息将从局部数据（每个单奇点）以一种有趣的数字数字造型和组合问题来获得。这种新方法的最重要特征是，它将导致一种完整的算法来找到所有封闭的表单解决方案。