Numerical methods for partial differential equations: algorithms and software on innovative computer architectures

偏微分方程的数值方法：创新计算机架构上的算法和软件

• 批准号: 89741-2010
• 负责人: Christara, Christina
• 金额: $ 1.82万
• 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: 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=521840
• 关键词: Numerical; methods; partial; differential; equations

Our world is comprised of physical and technological phenomena, objects and situations. In order to study the world, mathematical models are often used. These are usually equations, for example, ordinary or partial differential equations, linear or non-linear equations, integral equations,etc. The mathematical models are often insolvable by analytic mathematical techniques. Numerical methods are applied to solve or approximate the solution to mathematical models. These methods are implemented and run on computers. Numerical methods as well as computations may introduce errors. The computer results are studied and possible sources of errors are investigated. If the results are not satisfactory, either the mathematical model, or the numerical method to solve the model, or the computer program implementing the method have to be adjusted and the whole procedure repeated. Mathematical modelling, the development of numerical methods to solve mathematical models and the implementation of the methods on computers are important and wide areas of research, spanning computer science and mathematics, as well as physics and engineering.

我们的世界由物理和技术现象、物体和情况组成。为了研究世界，经常使用数学模型。这些通常是方程，例如，常微分方程或偏微分方程、线性或非线性方程、积分方程等。数学模型通常无法通过分析数学技术来求解。数值方法用于求解或近似数学模型的解。这些方法是在计算机上实现和运行的。数值方法和计算可能会引入误差。研究计算机结果并调查可能的错误来源。如果结果不令人满意，则必须调整数学模型，或求解模型的数值方法，或实施该方法的计算机程序，并重复整个过程。数学建模、解决数学模型的数值方法的发展以及这些方法在计算机上的实施是重要而广泛的研究领域，涵盖计算机科学和数学，以及物理和工程学。