非线性比例延迟微分方程隐式Euler法的数值稳定性  

Numerical Stability of Implicit Euler Method for Nonlinear Pantograph Equation

作　　者：余越昕[1] 

机构地区：[1]湘潭大学数学系,湖南湘潭411105

出　　处：《株洲工学院学报》2004年第5期21-23,共3页Journal of Zhuzhou Institute of Technology

基　　金：国家自然科学基金资助项目(批准号:10271100);湖南省教育厅资助科研项目

摘　　要：讨论非线性比例延迟微分方程隐式Euler法的数值稳定性,其中步长采用定步长和变步长两种方式。结果表明:在比例延迟微分方程真解是稳定或渐近稳定的条件下,定步长与变步长的隐式Euler法得到的数值解同样是稳定或渐近稳定的。This paper deals with the numerical stability of implicit Euler method for nonlinear pantograph equation in which constant stepsize and variable stepsize are applied. It is shown that the numerical solutions obtained from implicit Euler method with constant stepsize or variable stepsize are numerically stable or asymptotically stable when the condition that the analytical solution of the pantograph equation is stable or asymptotically stable holds.

关 键 词：比例延迟微分方程 隐式EULER法 数值稳定性 渐近稳定性 

分 类 号：O241[理学—计算数学]