We study a new sixth-order compact discretization using uniform three-grid point for the mildly nonlinear differential equation $$\phi ''=g(t,\phi )$$ , subject to the values of ϕ given at two end points of the regular solution interval. We also discuss three-step AGE (THAGE) iteration method as an application to the resulting difference equation as a powerful numerical computation device. In this algorithm, the common term is evaluated first to save the CPU time in comparison with the corresponding two-step algorithm. In addition, the error analysis is studied. Numerical performance is compared with the exact solution, and with the two-step AGE and SOR iteration methods.

中文翻译：

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一种新的三点六阶THAGE迭代法求解温和非线性两点边值问题的工程应用

我们研究了一种新的六阶紧致离散化，使用均匀的三网格点，用于轻度非线性微分方程 $$\phi ''=g(t,\phi )$$ ，受制于在两个端点给出的 ϕ 值正则求解区间。我们还讨论了三步 AGE (THAGE) 迭代方法，将其作为一种强大的数值计算设备应用于所得差分方程。在该算法中，与相应的两步算法相比，首先评估公共项以节省 CPU 时间。此外，还研究了误差分析。将数值性能与精确解以及两步 AGE 和 SOR 迭代方法进行比较。