Symbolic Computation and Differential Equations

符号计算和微分方程

• 批准号: 9322433
• 负责人: Michael Singer
• 金额: $ 8.66万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1998-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9322433&HistoricalAwards=false
• 关键词: Symbolic; Computation; Differential; Equations

This project develops symbolic algorithms to determine the algebraic structure of solutions of differential equations. In particular, the research includes the following: (i) Refine and extend algorithms for computing Galois groups of linear differential equations and algorithms for solving these equations in terms of classes of special functions; (ii) Develop algorithms to decide various properties of the Galois group. For example, give an algorithm to calculate the dimension of the group; (iii) Construct linear differential equations with a given Galois group; (iv) Develop improved algorithms to factor linear equations; and (v) Find first integrals of nonlinear systems of differential equations.

本计画发展符号演算法，以决定下列解的代数结构： 微分方程具体而言，研究包括以下内容： （一） 线性代数Galois群计算算法的改进与推广 微分方程和求解这些方程的算法 特殊功能; (ii)开发算法来决定各种 伽罗瓦群的性质 例如，给出一个算法来计算 集团的规模; (iii)构造线性微分方程， 一个给定的伽罗瓦群; (iv)开发改进的算法以分解线性 方程;以及 (v)求非线性方程的首次积分 微分方程组