刚性积分微分方程的几类高效隐式并行方法  

Several Classes of Efficient Numerical Implicit Parallel Methods for Solving Stiff Integro-Differential Equations

作　　者：刘红良[1] 李利娟[1] 李寿佛[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《湘潭大学自然科学学报》2006年第1期12-16,45,共6页Natural Science Journal of Xiangtan University

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

摘　　要：为求解刚性积分微分方程提供几类高效隐式并行方法,通过数值实验,进一步证实了李寿佛建立的刚性Volterra泛函微分方程数值方法B-理论有关猜想的正确性,同时通过对并行多值混合方法和Lobatto IIIC方法的数值结果进行分析和比较,发现李寿佛所创立的并行多值混合方法比Bellen极力推荐的Lobatto IIIC方法更具优势.Several classes of efficient numerical implicit parallel methods are recommended for solving stiff integro-differential equations, and the validity of B-theory of numerical methods for Volterra functional differential equations （VFDEs） presented by Li Shoofu in 2001 is further demonstrated by a series of numerical experiments using the methods recommended above. Furthermore, the characteristic and the advantages of parallel multivalue hybrid methods （PMHMs） and Lobatto ⅢC methods are illumiuated, respectively, by analysing and comparing the numerical results, the PMHM methods createa by Li Shoofu is superior to the Lobatto ⅢC mctheds.

关 键 词：刚性积分微分方程 泛函微分方程 高技并行方法 B-理论 

分 类 号：O241.81[理学—计算数学]