刚性泛函微分方程几类数值方法的测试和比较  

Test and Comparison of Numerical Methods for Stiff Volterra Functional Differential Equations

作　　者：樊华[1] 李林海[2] 聂勤务[3] 

机构地区：[1]湘潭大学数学与计算科学学院,湘潭411105 [2]湖南师范大学数学与计算机学院,长沙410081 [3]湖南科技大学,湘潭411201

出　　处：《系统仿真学报》2005年第3期609-612,共4页Journal of System Simulation

基　　金：国家 863 高技术惯性约束聚变主题;国家自然科学基金(批准号: 10271100)资助项目

摘　　要：为求解非线性刚性 Volterra 泛函微分方程推荐几类高效计算方法。通过数值试验进一步证实了李寿佛建立的泛函微分方程数值方法 B-理论及有关猜测的正确性。同时通过对数值结果进行分析和比较,详细说明了不同计算方法各自具有的特色和优势,为从事大规模刚性问题科学与工程计算的工程技术人员提供了选择计算方法的依据。Several classes of efficient numerical methods are recommended for solving nonlinear stiff Volterra functional differential equations (VFDEs), and the validity of B-theory of numerical methods for VFDEs presented by Li Shoufo in 2001 is further demonstrated by a series of numerical experiments using the methods recommended above. Furthermore, the characteristic and the advantages of the methods are illuminated, respectively, by analyzing and comparing the numerical results, which provides techniques for choosing numerical methods for the large scale stiff computation which appears in various scientific and engineering practical problems.

关 键 词：泛函微分方程 非线性刚性问题 高效数值方法 B-理论 数值测试 

分 类 号：O241.8[理学—计算数学]