一族奇异摄动时滞方程的有限差分法

Finite Difference Method for a Family of Singularly Perturbed Delay Differential Equations

考虑一族奇异摄动时滞微分方程.基于奇异摄动时滞方程准确解的性质,在分片等矩的Shishkin型网格上构造了线性奇异摄动时滞方程的有限差分格式,证得数值结果是关于小参数一致收敛的.应用牛顿拟线性法求解非线性奇异摄动时滞方程.数值实验证实了理论结果的准确性,进而表明该理论估计是稳健的.

Based on the property of analytical solution of singularly perturbed delay differential equation （SPDDE）, a finite difference scheme of linear SPDDE on the appropriate piecewise uniform Shishkin-type mesh is constructed. It is porved that the numerical result is ε uniform convergence in the maximum norm. Newton quasi-linearization method is used to solve the non-linear equations. Numerical results show the validity of the method.