Mathematical Sciences: Numerical Methods and Computer Software for Solving Integral Equations

数学科学：求解积分方程的数值方法和计算机软件

• 批准号: 9003287
• 负责人: Kendall Atkinson
• 金额: $ 6.4万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9003287&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Numerical; Methods; Computer

The research project is concerned with the numerical solution of several classes of linear and nonlinear integral equations. Specific types of integral equations slated for study include linear and nonlinear boundary integral equations, nonlinear Urysohn equations and nonlinear Fredholm equations. Such equations arise in a host of pure and applied areas, and one of the goals of the research is the development of multi-purpose codes that can be fitted into software routines to enable researchers from many different disciplines to solve these integral equations efficiently and accurately. Very often the solution of a problem in mathematical physics or mathematical biology can be expressed in the form of an integral equation. However this does not mean that the problem is solved; rather, the resulting integral equation must be solved either analytically or numerically. In this proposal the researchers will improve existing numerical schemes and develop new ones in order to produce multi-purpose software for the approximate solution of several types of integral equations in several space dimensions.

该研究项目涉及的数值解 几类线性和非线性积分方程。 指定用于研究的具体类型的积分方程包括 线性和非线性边界积分方程，非线性 Urysohn方程和非线性Fredholm方程。 等 方程出现在许多纯理论和应用领域，其中一个 研究的目标是开发多用途 可以安装到软件例程中的代码， 来自许多不同学科的研究人员来解决这些问题 积分方程的效率和准确性。 很多时候 数学物理或数学问题的解决 生物学可以用积分方程的形式表示。 然而，这并不意味着问题已经解决;相反， 所得的积分方程必须求解， 分析或数字。 在这项研究中，研究人员 将改进现有的数值方案，并在 为了生产多用途软件的近似 几类空间积分方程解 尺寸.