A family of explicit, semi-symmetric, eighth-order, six-step methods for the numerical solution of y″=f(x,y)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y^{\prime \prime }=f(x,y)$$\end{document} is considered. This family can be derived through interpolation techniques and only two stages (function evaluations) are spent per step. A method is given with variable coefficients. This variance is based in the requirement to nullify the errors when solving the standard simple oscillator. We conclude with numerical tests over a set of problems justifying our effort of dealing with the new method.

中文翻译：

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求解 $$y^{\prime \prime }=f(x,y)$$y″=f(x,y) 的八阶相位拟合六步法

y″=f(x,y)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \ 数值解的一系列显式、半对称、八阶、六步法usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y^{\prime \prime }= f(x,y)$$\end{document} 被考虑。这个族可以通过插值技术推导出来，每一步只花费两个阶段（函数评估）。给出了一种具有可变系数的方法。这种差异是基于在求解标准简单振荡器时消除误差的要求。我们以对一系列问题的数值测试作为结论，证明我们处理新方法的努力是合理的。