奇异摄动滞时微分方程的一致收敛数值方法(英文)

Uniformly Convergent Numerical Methods for Singularly Perturbed Delay Differential Equations

提出了求解线性奇异摄动滞时微分方程基于指数拟合技术的一致收敛和最佳一致收敛的数值方法,并证明了方法的一致收敛性。利用线性化的思想,并结合Newton-Raphson迭代,构造了求解非线性奇异摄动滞时微分方程相应的一致收敛的算法。数值例子验证上述理论结论的正确性。

Uniformly convergent and optimal uniformly convergent numerical schemes based on the exponential fitting technique were proposed for solving linear singular perturbation problems with afterffect. Corresponding uniformly convergent numerical schemes were constructed by linearization combined with Newton-Raphson iteration for nonlinear problems. Numerical examples were given to confirm the theoretical results.