Geometric numerical integration of differential equations

微分方程(DES)在模拟物理、生物、化学、天文学、气象学和地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来求解DES的新方法，这些方法比传统方法具有显著的优势，因为它们提供了关键的非线性稳定性。 该项目结合了来自6个国家的7名世界专家和1名早期职业研究人员，将使澳大利亚处于这一密集国际活动的前沿。 它将大大加强澳大利亚与数学软件行业(例如Wolfram Research，Inc.)的联系，并将带来世界级的毕业生和研究培训。

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.