延迟微分方程指数Rosenbrock方法的渐近稳定性

Asymptotic stability of exponential rosenbrock methods for delay differential equations

改造求解常微分方程的指数Rosenbrock方法,利用K.J.In’t Hout的插值技巧,构造求解延迟微分方程的一类指数Rosenbrock方法,证明这类方法是GP-稳定的充要条件是相应地求解常微分方程的指数Rosenbrock方法是A-稳定的。数值实验表明这类方法是有效的。

Delay differential equations extensively appeared in physics and engineering, biology, medicine and economic fields, and it is no doubt that the numerical method about solving delay differential equation is important. In recent years, the asymptotic stability of numerical method has caused many scholars＂ attention. By using K. J. In＇t Hour＇ s interpolation techniques, the exponential rosenbrock methods for delay differential equations are constructed through appropriate modification of the exponential rosenbrock method for ordinary differential equations. Morever, GP-stability of this class of method is equivalent to A-stability of rosenbrock methods in the numerical of ordinary differential equations. Finally, numerical experiments show that the method is effective.