Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations

Jator S. N.; Ngwane F. F.; Kirby N. O.

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Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations

机译：求解通用振荡二阶初值问题和双曲线偏微分方程的功能拟合块方法

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We present a block hybrid functionally fitted Runge-Kutta-Nystrom method (BHFNM) which is dependent on the stepsize and a fixed frequency. Since the method is implemented in a block-by-block fashion, the method does not require starting values and predictors inherent to other predictor-corrector methods. Upon deriving our method, stability is illustrated, and it is used to numerically solve the general second-order initial value problems as well as hyperbolic partial differential equations. In doing so, we demonstrate the method's relative accuracy and efficiency.

机译：我们介绍了一个块混合功能拟合的跳动-Kutta-Nystrom方法（BHFNM），其取决于步骤和固定频率。由于该方法以逐个块的方式实现，因此该方法不要求其他预测器校正器方法固有的起始值和预测器。在得出我们的方法时，示出了稳定性，并且它用于在数值上解决一般的二阶初始值问题以及双曲线部分微分方程。在这样做时，我们展示了该方法的相对准确性和效率。

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《Mathematical Problems in Engineering》 |2019年第5期|1535430.1-1535430.14|共14页
作者
Jator S. N.; Ngwane F. F.; Kirby N. O.;
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Austin Peay State Univ Dept Math & Stat Clarksville TN 37044 USA;

Univ South Carolina Dept Math Walterboro SC 29488 USA;

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

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1. Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations [J] . Jator S. N., Ngwane F. F., Kirby N. O. Mathematical Problems in Engineering . 2019,第PTa5期

机译：求解广义振动二阶初值问题和双曲型偏微分方程的函数拟合块法
2. Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations [J] . S. N. Jator, F. F. Ngwane, N. O. Kirby Mathematical Problems in Engineering: Theory, Methods and Applications . 2019,第1期

机译：求解通用振荡二阶初值问题和双曲线偏微分方程的功能拟合块方法
3. A Trigonometrically Fitted Block Method for Solving Oscillatory Second-Order Initial Value Problems and Hamiltonian Systems [J] . F. F. Ngwane, S. N. Jator International Journal of Differential Equations . 2017,第期

机译：用于解决振荡二阶初值问题和哈密顿系统的三角拟合块方法
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. Shooting method-based algorithms for solving control problems associated with second-order hyperbolic partial differential equations. [D] . Luo, BiYong. 2001

机译：基于射击方法的算法，用于解决与二阶双曲型偏微分方程有关的控制问题。
6. A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations [O] . T. A. Biala, S. N. Jator -1

机译：求解非线性椭圆和双曲偏微分方程的边值方法
7. Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations [O] . S. N. Jator, F. F. Ngwane, N. O. Kirby 2019

机译：求解通用振荡二阶初值问题和双曲线偏微分方程的功能拟合块方法

Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations

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