求解非线性复合刚性脉冲微分方程的Euler分裂方法

EULER SPLITTING METHOD FOR SOLVING NONLINEAR COMPOSITE STIFF IMPULSIVE DIFFERENTIAL EQUATIONS

针对非线性复合刚性脉冲微分方程,对其非刚性部分采用显式Euler方法求解,对其刚性部分采用隐式Euler方法求解,得到了求解问题的Euler分裂方法,研究了该方法的稳定性和收敛性.数值试验验证了所获理论的正确性,同时也表明该方法能显著提升计算速度.

For nonlinear composite stiff impulsive differential equations,explicit Euler method is used to solve the non-stif part,and implicit Euler method is used to solve the stiff part.Then Euler splitting method is obtained,and the stability and convergence of the method are studied.The correctness of the obtained theory is verified by numerical experiments.It also shows that this method can significantly improve the computational speed.