Numerical Solution of Linear Klein-Gordon Equation using FDAM Scheme

机译：使用FDAM方案的线性Klein-Gordon方程的数值解

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Many scientific areas appear in a hyperbolic partial differential equation like the Klien-Gordon equation. The analytical solutions of the Klein-Gordon equation have been approximated by the suggested numerical approaches. However, the arithmetic mean (AM) method has not been studied on the Klein-Gordon equation. In this study, a new proposed scheme has utilized central finite difference formula in time and space (CTCS) incorporated with AM formula averaging of functional values for approximating the solutions of the Klein-Gordon equation. Three-point AM is considered to a linear inhomogeneous Klein-Gordon equation. The theoretical aspects of the numerical scheme for the Klein-Gordon equation are also considered. The stability analysis is analyzed by using von Neumann stability analysis and Miller Norm Lemma. Graphical results verify the necessary conditions of Miller Norm Lemma. Good results obtained relate to the theoretical aspects of the numerical scheme. The numerical experiments are examined to verify the theoretical analysis. Comparative study shows the new CTCS scheme incorporated with three-point AM method produced better accuracy and shown its reliable and efficient over the standard CTCS scheme.

机译：许多科学领域出现在像Klien-Gordon方程等双曲线部分微分方程中。 Klein-Gordon方程的分析解已经通过建议的数值方法来近似。然而，算术平均值（AM）方法尚未对Klein-Gordon方程进行研究。在该研究中，一种新的提出方案在时间和空间（CTC）中利用了中央有限差分公式，其与AM公式平均的功能值平均，以近似Klein-Gordon方程的溶液。三点am被认为是线性不均匀的Klein-Gordon方程。还考虑了Klein-Gordon方程数值方案的理论方面。通过使用von neumann稳定性分析和米勒规范引理来分析稳定性分析。图形结果验证了Miller Norm Lemma的必要条件。获得的良好结果涉及数值方案的理论方面。检查数值实验以验证理论分析。比较研究表明，新的CTCS方案加入了三点AM方法，生产了更好的准确性，并在标准CTCS方案上显示了其可靠和有效的。

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《International Conference on Education, Mathematics and Science》|2017年|1 v. (various pagings) :|共6页
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Noraini Kasron; Erni Suryani Suharto; Ros Fadilah Deraman; Khairil Iskandar Othman; Mohd Agos Salim Nasir;
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中图分类 O1-532;
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finite difference scheme; Klein-Gordon equation; arithmetic mean; stability; consistency; convergence;

机译：有限差分方案;Klein-Gordon方程;算术平均值;稳定性;一致性;收敛;

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1. Numerical Solution of the Nonlinear Klein-Gordon Equation Using Multiquadric Quasi-interpolation Scheme [J] . M. Sarboland, A. Aminataei Universal Journal of Applied Mathematics . 2015,第3期

机译：二次拟插值法求解非线性Klein-Gordon方程的数值解
2. In this paper, we implement the fractional complex transform method to convert the nonlinear fractional Klein-Gordon equation (FKGE) to an ordinary differential equation. We use the variational iteration method (VIM) to solve the resulting ODE. The fractional derivatives are presented in terms of the Caputo sense. Some numerical examples are presented to validate the proposed techniques. Finally, a comparison with the numerical solution using Runge-Kutta of order four is given. [J] . M. M. Khader, M. Adel Nonlinear engineering: Modeling and application . 2016,第3期

机译：在本文中，我们采用分数阶复杂变换方法将非线性分数阶Klein-Gordon方程（FKGE）转换为常微分方程。我们使用变分迭代方法（VIM）来解决所得的ODE。分数导数以Caputo形式表示。提出了一些数值例子来验证所提出的技术。最后，与使用四阶Runge-Kutta的数值解进行了比较。
3. A numerical scheme based on differential quadrature method for numerical simulation of nonlinear Klein-Gordon equation [J] . Anjali Verma, Ram Jiwari, Satish Kumar International journal of numerical methods for heat & fluid flow . 2014,第7期

机译：基于微分求积法的非线性Klein-Gordon方程数值模拟方案
4. Numerical Solution of Linear Klein-Gordon Equation using FDAM Scheme [C] . Noraini Kasron, Erni Suryani Suharto, Ros Fadilah Deraman, International Conference on Education, Mathematics and Science . 2017

机译：使用FDAM方案的线性Klein-Gordon方程的数值解
5. Global Existence of Solutions to Semilinear Klein-Gordon Equations [D] . Pikula, Nina. 2019

机译：半线性Klein-Gordon方程解的整体存在性
6. Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and coupled Klein-Gordon equations [O] . Kamruzzaman Khan, M Ali Akbar, S M Rayhanul Islam -1

机译：（1 + 1）维非线性色散修正的Benjamin-Bona-Mahony方程和Klein-Gordon耦合方程的精确解
7. Numerical Solution of the Nonlinear Klein-Gordon Equation Using Multiquadric Quasi-interpolation Scheme [O] . M. Sarboland, A. Aminataei 2015

机译：使用型多功率准插值方案的非线性Klein-Gordon方程的数值解

Numerical Solution of Linear Klein-Gordon Equation using FDAM Scheme

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