一类变时滞微分代数方程单支方法的收敛性  

CONVERGENCE OF ONE-LEG METHODS FOR A CLASS OF VARIABLE RETARDED DIFFERENTIAL ALGEBRAIC EQUATIONS

作　　者：肖飞雁[1] 张诚坚[1] 

机构地区：[1]华中科技大学数学系,武汉430074

出　　处：《数值计算与计算机应用》2008年第3期217-225,共9页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(10571066)

摘　　要：B-收敛和D-收敛的概念被推广到了变时滞微分代数方程问题,给出了D_A-收敛的定义,讨论了该类问题的D_A-收敛性,并给出了相应的误差估计,证明了如果G-稳定的单支方法对于常微分方程初值问题在经典意义下是p阶相容的且(βκ/ακ)>0,那么具有线性插值过程的该方法是p阶D_A-收敛的,这里p=1或2。This paper extends B-convergence and D-convergence to a class of variable retarded dif- ferential algebraic equations and puts forward DA-convergence. Furthermore, DA-convergence of the problem is discussed and its error estimation is given. Finally, it is proved that a One- Leg method with linear interpolation procedure is DA-convergent of order p if it is G-stable and consistent of order p for ordinary differential equations and βκ/ακ〉0,here p=1 or 2.

关 键 词：变时滞微分代数方程 单支方法 G-稳定 D-收敛 

分 类 号：O175[理学—数学]