Integrating Oscillatory General Second-Order Initial Value Problems Using a Block Hybrid Method of Order 11

Jator Samuel N.; King Kindyl L.

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Integrating Oscillatory General Second-Order Initial Value Problems Using a Block Hybrid Method of Order 11

机译：使用11阶块混合方法积分振动一般二阶初值问题

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In some cases, high-order methods are known to provide greater accuracy with larger step-sizes than lower order methods. Hence, in this paper, we present a Block Hybrid Method (BHM) of order 11 for directly solving systems of general second-order initial value problems (IVPs), including Hamiltonian systems and partial differential equations (PDEs), which arise in multiple areas of science and engineering. The BHM is formulated from a continuous scheme based on a hybrid method of a linear multistep type with several off-grid points and then implemented in a block-by-block manner. The properties of the BHM are discussed and the performance of the method is demonstrated on some numerical examples. In particular, the superiority of the BHM over the Generalized Adams Method (GAM) of order 11 is established numerically.

机译：在某些情况下，已知高阶方法与低阶方法相比，具有更大的步长和更大的精度。因此，在本文中，我们提出了一种11阶的块混合方法（BHM），用于直接求解一般的二阶初值问题（IVP）的系统，包括哈密顿系统和偏微分方程（PDE），它们在多个区域中都出现科学和工程学。 BHM是基于具有多个离网点的线性多步类型混合方法的连续方案制定的，然后以逐块方式实施。讨论了BHM的性质，并在一些数值示例上证明了该方法的性能。特别地，在数值上建立了BHM优于11阶广义亚当斯方法（GAM）的优势。

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《Mathematical Problems in Engineering》 |2018年第7期|3750274.1-3750274.15|共15页
作者
Jator Samuel N.; King Kindyl L.;
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Austin Peay State Univ, Dept Math & Stat, Clarksville, TN 37044 USA;

Austin Peay State Univ, Dept Math & Stat, Clarksville, TN 37044 USA;

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1. Integrating Oscillatory General Second-Order Initial Value Problems Using a Block Hybrid Method of Order 11 [J] . Samuel N. Jator, Kindyl L. King Mathematical Problems in Engineering: Theory, Methods and Applications . 2018,第4期

机译：使用11阶块混合方法积分振动性一般二阶初值问题
2. Trigonometrically fitted multi-step hybrid methods for oscillatory special second-order initial value problems [J] . Li Jiyong, Lu Ming, Qi Xuli International journal of computer mathematics . 2018,第5a8期

机译：三角拟合多步混合法求解特殊的二阶振动初值问题
3. Multi-step hybrid methods adapted to the numerical integration of oscillatory second-order systems [J] . Jiyong Li Journal of Applied Mathematics and Computing . 2019,第1a2期

机译：多步混合方法适用于振荡二阶系统的数值集成
4. A Trigonometrically Fitted Optimized Two-step Hybrid Block Method for Solving Initial-value Problems of the Form y" = f(x,y,y') with Oscillatory Solutions [C] . Higinio Ramos, Z. Kalogiratou, Th. Monovasilis, International Conference on Numerical Analysis and Applied Mathematics . 2015

机译：具有振荡溶液的求解y“= f（x，y，y'）的初始值问题的三角拟合的两步混合块方法
5. Linear second-order system solution accuracies with digital, analog and hybrid computer methods. [D] . Camire, Guy A. 1983

机译：线性二阶系统解决方案具有数字，模拟和混合计算机方法的精度。
6. Does Determination of Initial Cluster Centroids Improve the Performance of K-Means Clustering Algorithm? Comparison of Three Hybrid Methods by Genetic Algorithm Minimum Spanning Tree and Hierarchical Clustering in an Applied Study [O] . Saeedeh Pourahmad, Atefeh Basirat, Amir Rahimi, 2020

机译：初始簇质心的确定是否提高了K-Means聚类算法的性能？应用研究中遗传算法最小生成树和分层聚类的三种混合方法的比较
7. Integrating Oscillatory General Second-Order Initial Value Problems Using a Block Hybrid Method of Order 11 [O] . Samuel N. Jator, Kindyl L. King 2018

机译：使用块混合序列11的振荡一般二阶初始值问题集成了振荡的一般二阶初始值问题
8. Detection and Integration of Oscillatory Differential Equations with Initial Stepsize, Order and Method Selection [R] . Gallivan, K. A. 1980

机译：具有初始步长，阶数和方法选择的振动微分方程的检测与积分

Integrating Oscillatory General Second-Order Initial Value Problems Using a Block Hybrid Method of Order 11

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