Software for Error Controlled Numerical Solution of Boundary Value Ordinary Differential Equations and Parabolic Partial Differential Equations

边值常微分方程和抛物型偏微分方程误差控制数值求解软件

• 批准号: 946-2012
• 负责人: Muir, Paul
• 金额: $ 1.6万
• 依托单位: Saint Mary's University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=520326
• 关键词: Software; Error; Controlled; Numerical; Solution

Along with theoretical and experimental science, computational modeling is now viewed as a third fundamental branch of scientific inquiry. A majority of computational models, arising in such areas as chemistry, physics, biology, and finance, involve complex systems of differential equations (DEs), for which approximate solutions are obtained through the use of sophisticated numerical software. Because the numerical solutions are approximate, it is essential that the software also assess the quality of the computed solution. Two popular types of assessment are the global error (the difference between the approximate and exact solutions) and the defect (the amount by which the numerical solution fails to satisfy the equations). Good quality software will adapt a computation so that the numerical solution can be obtained efficiently and so that an estimate of the global error or defect satisfies a user-provided tolerance.

沿着理论和实验科学，计算建模现在被视为科学探究的第三个基本分支。在化学、物理、生物和金融等领域中出现的大多数计算模型都涉及复杂的微分方程（DE）系统，其近似解是通过使用复杂的数值软件获得的。 由于数值解是近似的，因此软件还必须评估计算解的质量。两种流行的评估类型是全局误差（近似解和精确解之间的差异）和缺陷（数值解不满足方程的量）。高质量的软件将调整计算，使得可以有效地获得数值解，并且使得全局误差或缺陷的估计满足用户提供的公差。