Computational and Applied Mathematics ( IF 2.5 ) Pub Date : 2023-10-06 , DOI: 10.1007/s40314-023-02463-y
R. I. Abdulganiy , H. Ramos , J. A. Osilagun , S. A. Okunuga , Sania Qureshi
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For the approximate solution of the Kepler equations and some related problems, a fourth-order convergent functionally-fitted block hybrid Falkner method which is based on the concepts of interpolation and collocation of the fitting function given as a linear combination of \(\left\{ 1,\sin (\omega x),\cos (\omega x),\sinh (\omega x),\cosh (\omega x)\right\} \) is presented. The proposed method uses variable coefficients that are based on the product of the dominant frequency and the integration step length. This hybrid formula uses a block-wise implementation strategy to get over the difficulties of the predictor–corrector mode. In addition to being zero stable, the proposed method is applied to the Lambert–Watson linear stability test, which allows obtaining its stability region. Six numerical examples are provided to establish the performance of the proposed method.
中文翻译:
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开普勒方程及相关问题的函数拟合块混合 Falkner 方法
对于开普勒方程和一些相关问题的近似解,提出了一种四阶收敛函数拟合块混合 Falkner 方法,该方法基于以 \(\left\ 的线性组合形式给出的拟合函数的插值和配置概念{ 1,\sin (\omega x),\cos (\omega x),\sinh (\omega x),\cosh (\omega x)\right\} \)被呈现。所提出的方法使用基于主频率和积分步长的乘积的可变系数。该混合公式使用分块实现策略来克服预测器-校正器模式的困难。除了零稳定之外,所提出的方法还应用于兰伯特-沃森线性稳定性测试,从而可以获得其稳定区域。提供了六个数值示例来确定所提出方法的性能。