CISE-CCF-AF-Algebra: SGER: Computational Methods for Systems of Difference Equations

CISE-CCF-AF-代数：SGER：差分方程组的计算方法

• 批准号: 0964875
• 负责人: Alexey Ovchinnikov
• 金额: --
• 依托单位: CUNY Queens College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-16 至 2010-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0964875&HistoricalAwards=false
• 关键词: CISE; CCF; AF; Algebra; SGER

Alexey I. Ovchinnikov proposes to develop efficient algorithms that determine the differential, difference, and algebraic structure of solutions of difference equations using methods of differential, difference, and computer algebra. The investigator has successfully contributed to the development of computational differential ideal theory and the Galois theory of linear differential equations. He will apply these results and methods to give efficient algorithms that compute properties of systems of difference equations. These properties are reflected in characteristic sets and Galois groups of the equations. In particular, the investigator will develop algorithms to reduce systems of non-linear difference equations to simpler systems. These algorithms test consistency of the input system and eliminate variables from the equations of the system. He will also give a Galois theory of linear difference equations with difference parameters to study difference algebraic dependences among solutions of difference equations.

阿列克谢岛Ovchinnikov提出开发有效的算法，确定差分方程的差分，差分和代数结构的解决方案，使用微分，差分和计算机代数的方法。研究者成功地为发展计算微分理想理论和线性微分方程的伽罗瓦理论做出了贡献。他将应用这些结果和方法，给出有效的算法，计算差分方程系统的属性。这些性质反映在方程的特征集和伽罗瓦群中。 特别是，研究人员将开发算法，以减少系统的非线性差分方程更简单的系统。这些算法测试输入系统的一致性，并从系统的方程中消除变量。他还将给伽罗瓦理论的线性差分方程的差异参数研究差分方程的解决方案之间的差异代数依赖。