刚性振荡问题并行多值混合方法的指数拟合及其应用  

Exponential Fitting Parallel Multivalue Hybrid Methods for Stiff Oscillatory Problems

作　　者：张模蕴[1] 肖爱国[2] 

机构地区：[1]湘潭大学机械工程学院,湖南湘潭411105 [2]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》2010年第1期5-11,共7页Natural Science Journal of Xiangtan University

基　　金：国家自科基金项目(10971175);教育部博士点基金项目(20094301110001);湖南省自科基金项目(09JJ3002)

摘　　要：针对刚性振荡问题,构造二至三步并行多值混合方法的指数拟合算法,分析其稳定性,表明所构造的指数拟合方法EF-II-2、EF-II-3有很好的零稳定性和绝对稳定性.同时考虑将此算法扩展到向量方程后系数的计算问题.数值试验显示了所构造算法的高效性,表明所构造的新算法的确比相应的并行多值混合方法对刚性振荡问题更为有效.For stiff oscillatory problems, we constructed some exponential fitting algorithms of two-step and three-step parallel multivalue hybrid methods and analyze their stability. It is shown that the exponential fitting parallel multivalue hybrid algorithms EF-II-2 and EF-II-3 possess good 0-stability and absolute stability. Meanwhile, we discussed the coefficient computation of the new methods after we extended these algorithms to vector equations. Numerical examples show high efficiency of the proposed methods. Also it is shown the new algorithms are more effective than the corresponding parallel multivalue hybrid methods for stiff oscillatory problems.

关 键 词：刚性问题 振荡问题 并行多值混合方法 指数拟合 稳定性 

分 类 号：O241.81[理学—计算数学]