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.
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
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
delay differential equations with a proportional delay
linear multistep methods
compound trapezoidal rule
dissipativity
