刚性Volterra泛函微分方程梯形方法的B-理论  

B-THEORY OF TRAPEZOID FORMULA FOR STIFF VOLTERRA FUNCTIONAL DIFFERENTIAL EQUATIONS

作　　者：余越昕[1] 李寿佛[1] 

机构地区：[1]湘潭大学数学系,湖南湘潭411105

出　　处：《计算数学》2007年第4期359-366,共8页Mathematica Numerica Sinica

基　　金：国家自科基金项目(10271100);湖南省教育厅科研资助优秀青年项目

摘　　要：最近,李寿佛建立了刚性Volterra泛函微分方程Runge_Kutta方法和一般线性方法的B-理论,其中代数稳定是数值方法B-稳定与B-收敛的首要条件,但梯形方法表示成Runge—Kutta方法的形式或一般线性方法的形式都不是代数稳定的,因此上述理论不适用于梯形方法.本文从另一途径出发,证明求解刚性Volterra泛函微分方程的梯形方法是B-稳定且2阶最佳B-收敛的,最后的数值试验验证了所获理论的正确性.Recently, B-theory of Runge-Kutta methods and general linear methods for stiff Volterra functional differential equations was established by Li. The algebraically stable of the numerical methods is the chief condition that guarantees the methods to be B-stable and B-convergent. However, the trapezoid formula isn＇t algebraically stable, whether it expresses as the form of Runge-Kutta methods or as the form of general linear methods. Thus, the afore-mentioned theory is not suitable for the trapezoid formula. It is proved in the present paper that the trapezoid formula is B-stable and optimally B-convergent of order 2 by another approach. A numerical test that confirms the theoretical results is given in the end.

关 键 词：刚性Volterra泛函微分方程 梯形方法 B-稳定 B-收敛 

分 类 号：O241.8[理学—计算数学]