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Algorithms for Solving Linear Recurrence Equations

Algorithms for Solving Linear Recurrence Equations
求解线性递推方程的算法
批准号:
9805983
负责人:
Mark van Hoeij
金额:
$4.18万
依托单位:
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
1998
资助国家:
美国
项目状态:
已结题
起止时间:
1998-06-15 至 2001-05-31

项目摘要

项目成果

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中文摘要
翻译
Van HoeijDifference方程(即递归方程)与微分方程有许多共同的性质。PI最近引入了差分方程组的有限奇点的概念。有了这个概念,现在可以将更多的微分方程组方法应用到差分方程组中,这就产生了新的算法。特别是,PI旨在实现一种新的高效算法来计算递归方程的超几何解。这些算法有几个应用,如寻找和证明公式,或求解某些线性微分方程组。
英文摘要
9805983van HoeijDifference equations (i.e. recurrence equations) have a number of properties in common with differential equations. The PI recently introduced the notion of finite singularities of difference equations. With this notion, more methods for differential equations can now be applied to difference equations, and this leads to new algorithms. In particular, the PI intends to implement a new efficient algorithm for computing hypergeometric solutions of recurrence equations. These algorithms have several applications, such as finding and proving formulas, or solving certain linear differential equations.
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AF: Small: Solving and Simplifying Algebraic, Differential, and Difference Equations.
  • 批准号:
    2007959
  • 项目类别:
    Standard Grant
  • 资助金额:
    $35.0万
  • 财政年份:
    2020
  • 负责人:
    Mark van Hoeij
  • 依托单位:
AF: Small: A-Hypergeometric Solutions of Linear Differential Equations
  • 批准号:
    1618657
  • 项目类别:
    Standard Grant
  • 资助金额:
    $45.0万
  • 财政年份:
    2016
  • 负责人:
    Mark van Hoeij
  • 依托单位:
AF:Small: Linear Differential Equations with a Convergent Integer Series Solution
  • 批准号:
    1319547
  • 项目类别:
    Standard Grant
  • 资助金额:
    $47.94万
  • 财政年份:
    2013
  • 负责人:
    Mark van Hoeij
  • 依托单位:
AF: Small: Solving Linear Differential in Terms of Special Functions
  • 批准号:
    1017880
  • 项目类别:
    Standard Grant
  • 资助金额:
    $39.61万
  • 财政年份:
    2010
  • 负责人:
    Mark van Hoeij
  • 依托单位:
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