Mathematical Sciences: Studies in Numerical Solution of Functional Differential Equations

数学科学：泛函微分方程数值解的研究

• 批准号: 9208048
• 负责人: Zdzislaw Jackiewicz
• 金额: $ 12.7万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-15 至 1996-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9208048&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Numerical; Solution

The purpose of the research is to study the properties of numerical methods for ordinary and functional differential equations and Volterra integral and integrodifferential equations. An efficient and reliable general purpose algorithm for the numerical solution of neutral delay-differential equations and Volterra integro-differential equations based on variable stepsize variable order Adams formulas will be developed. The asymptotic behavior of recurrence relations resulting from application of various numerical methods to Volterra integral and integro-differential equations with nonconvolution kernels will be studied. Moreover, convergence, order and stability properties of time-point relaxations and waveform relaxation Runge-Kutta methods for large systems of ordinary differential equations will be examined. These methods are appropriate in a parallel computing environment. Finally, variable stepsize two-step Runge-Kutta methods for differential equations will be investigated. One of the main applications of these methods is to provide efficient error estimates for continuous Runge-Kutta methods. This research is in the area of numerical analysis, which has applications to a wide variety of physical and engineering applications.

本研究的目的是研究 常微分和泛函微分数值方法 方程与沃尔泰拉积分微分 方程 一种高效可靠的通用算法 中立型时滞微分方程的数值解 方程和沃尔泰拉积分微分方程的基础上， 变步长变阶亚当斯公式 开发 递推关系的渐近性 由于应用各种数值方法， 带积分项的沃尔泰拉积分微分方程 非卷积核将被研究。 此外，收敛， 时间点弛豫的顺序和稳定性， 波形松弛Runge-Kutta方法在大系统中的应用 将研究常微分方程。 这些方法 适用于并行计算环境。 最后， 微分方程的变步长两步Runge-Kutta方法 方程将被研究。 的主要应用之一 这些方法是为了提供有效的误差估计， 连续Runge-Kutta方法 本研究属于数值分析领域， 应用于各种物理和工程 应用.