GEOMETRIC NUMERICAL INTEGRATION

几何数值积分

• 批准号: ARC : DP0210300
• 负责人: A/Prof Gilles Quispel
• 金额: $ 23万
• 依托单位: La Trobe University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2002
• 资助国家: 澳大利亚
• 起止时间: 2002-01-01 至 2005-12-31
• 项目状态: 已结题
• 来源: https://researchdata.edu.au/geometric-numerical-integration/72798
• 关键词: GEOMETRIC; NUMERICAL; INTEGRATION

GEOMETRIC NUMERICAL INTEGRATION. Many scientific phenomena in physics, astronomy, and chemistry, are modelled by ordinary differential equations (ODEs). Often these equations have no solution in closed form, and one relies on numerical integration. Traditionally this is done using Runge-Kutta methods or linear multistep methods. In the last decade, however, we (and others) have discovered novel classes of so-called "geometric" numerical integration methods that preserve qualititative features of certain ODE's exactly (in contrast to traditional methods), leading to crucial stability improvements. Extending concepts from dynamical systems theory and traditional numerical ODEs, this project will improve, extend and systematize this new field of geometric integration.

几何数值积分。物理学、天文学和化学中的许多科学现象都是用常微分方程 (ODE) 建模的。通常这些方程没有封闭形式的解，并且依赖于数值积分。传统上，这是使用龙格-库塔方法或线性多步方法来完成的。然而，在过去十年中，我们（和其他人）发现了新型所谓的“几何”数值积分方法，这些方法准确地保留了某些 ODE 的定性特征（与传统方法相比），从而带来了关键的稳定性改进。该项目扩展了动力系统理论和传统数值常微分方程的概念，将改进、扩展和系统化几何积分这一新领域。