一类求解比例延迟积分微分方程线性多步法的散逸性  

Dissipativity of Linear Multistep Methods for Delay-integro-differential Equations with a Proportional Delay

作　　者：祁锐[1] 何汉林[1] 

机构地区：[1]海军工程大学理学院,武汉430033

出　　处：《计算机与数字工程》2012年第7期1-2,59,共3页Computer & Digital Engineering

基　　金：国家自然科学基金资助项目(编号:60974136);海军工程大学自然科学基金(编号:HGDQNEQJJ11002)资助

摘　　要：考虑了比例延迟积分微分方程的数值方法的散逸性。首先,通过变换将原方程变为常延迟积分微分方程,然后把一类线性多步法应用到以上问题中,用线性插值程序和复合梯形公式分别逼近延迟项和积分项,证明了在一定条件下,该数值方法具有散逸性。Numerical dissipativity of delay differential equations with a propo- rtional delay is concerned. At first, the original equations can be transformed into the constant delay integro-differential equations by a change of the independent conversion, and then we apply a class of linear multistep methods is applied to the above problems,it is proved in some proper conditions that the numerical solution is dissipative for a class of linear multistep methods when linear interpolation and compound trapezoidal rule denote approximations to delay term and integration term, respectively.

关 键 词：比例延迟积分微分方程 线性多步法 复合梯形公式 散逸性 

分 类 号：O241.8[理学—计算数学]