刚性多滞量积分微分方程的BDF方法  

BDF METHODS FOR STIFF MULTI-DELAY INTEGRO-DIFFERENTIAL EQUATIONS

作　　者：张诚坚[1] 何耀耀[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》2007年第2期124-132,共9页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(编号10571066);教育部回国留学人员基金.

摘　　要：本文研究了求解刚性多滞量Volterra型积分微分方程的BDF方法的非线性稳定性和计算有效性．经典BDF方法被改造用于求解一类刚性多滞量Volterra型积分微分方程,数值试验表明所给出的方法是高度有效的．此外,证明了在适当条件下,其扩展的BDF方法是渐近稳定和整体稳定的．This paper deals with nonlinear stability and computational effectiveness of BDF methods for solving stiff multi-delay integro-differential equations of Volterra type. The classical BDF methods are adapted to a class of nonlinear stiff multidelay integro-differential equations of Volterra type, and the numerical experiments show that the presented methods are highly effective. Moreover, it is proven under the suitable conditions that the extended BDF methods are globally and asymptotically stable.

关 键 词：刚性多滞量Volterra型积分微分方程 BDF方法 数值稳定性 

分 类 号：O241.8[理学—计算数学]