Robust and reliable software for the numerical solution of ODEs

用于 ODE 数值求解的强大而可靠的软件

• 批准号: 8644-2006
• 负责人: Enright, Wayne
• 金额: $ 3.79万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=366476
• 关键词: Robust; reliable; software; numerical; solution

We plan to analyze and improve the reliability and robustness of numerical methods for differential equations -- both ordinary differential equations (ODEs) and partial differential equations (PDEs).We also plan to analyze and develop effective tools for the visualization and verification of approximate solutions to differential equations. We will identify and quantify the key trade-off that arises between efficiency and reliability. Where possible we will implement methods which allow the user to select from a small menu of available error control strategies. The more expensive strategies will produce approximate solutions that are more likely to have an accuracy that is consistent with the prescribed tolerance.

我们计划分析和提高微分方程数值方法的可靠性和鲁棒性-包括常微分方程（ODE）和偏微分方程（PDE）。我们还计划分析和开发有效的工具，用于微分方程近似解的可视化和验证。我们将确定并量化效率和可靠性之间的关键权衡。在可能的情况下，我们将实现允许用户从可用错误控制策略的小菜单中选择的方法。更昂贵的策略将产生近似的解决方案，更有可能具有与规定的公差一致的精度。