Geometric numerical integration of differential equations

微分方程的几何数值积分

• 批准号: DP0878459
• 负责人: Prof Reinout Quispel
• 金额: $ 57.73万
• 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: 2008
• 资助国家: 澳大利亚
• 起止时间: 2008-05-30 至 2013-05-29
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0878459
• 关键词: Geometric; numerical; integration; differential; equations

Differential equations (DEs) play a central role in modelling scientific phenomena in physics, biology, chemistry, astronomy, meteorology, and geoscience. We have developed new ways of solving DEs, using geometric integration, which have significant advantages over traditional methods because of the crucial nonlinear stability they provide. This project, combining 7 world experts from 6 countries and 1 early career researcher, will place Australia at the forefront of this intensive international activity. It will significantly strengthen Australia's links with the mathematical software industry (e.g. Wolfram Research, Inc), and will lead to world class graduates and research training.

微分方程 (DE) 在模拟物理、生物学、化学、天文学、气象学和地球科学中的科学现象方面发挥着核心作用。我们开发了使用几何积分求解微分方程的新方法，由于其提供了至关重要的非线性稳定性，因此与传统方法相比具有显着优势。 该项目由来自 6 个国家的 7 名世界专家和 1 名早期职业研究员组成，将使澳大利亚处于这一密集国际活动的最前沿。 它将显着加强澳大利亚与数学软件行业（例如 Wolfram Research, Inc）的联系，并将带来世界一流的毕业生和研究培训。