四阶非线性奇摄动问题的差分解法

Difference Schemes for a Fourth Order Nonlinear Singular Perturbation Problem

本文考虑了一类四阶非线性方程边值问值的奇摄动问题。建立一个带拟合因子的差分格式，利用多重尺度法求得了微分方程的渐近解。证明所建立的差分格式在最大模意义下的一致收敛性及一致误差估计．最后给出一个具有二次敛速的求解非线性方程组的选代算法及一个例子的数值计算结果．

In this paper, the author considered the singular perturbation problem for a fourth-ordernonlinear ordinary differential equation with boundary conditions,establishthe difference scheme with a fitting factor and applied the method of multiple scales to obtain the asymptotic solution of the differential equation. prove that the difference scheme is uniformly convergent in L∞ norm and give the uniform error estimates. Finally, the author propose the iterative computing method with quadratic convergence rate for solving the nonlinear equations and present numerical results for illustration