A New Approach to Numerical Solution of Nonlinear Klein-Gordon Equation

Berna Buelbuel; Mehmet Sezer

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A New Approach to Numerical Solution of Nonlinear Klein-Gordon Equation

机译：非线性Klein-Gordon方程数值解的新方法

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A numerical method based on collocation points is developed to solve the nonlinear Klein-Gordon equations by using the Taylor matrix method. The method is applied to some test examples and the numerical results are compared with the exact solutions. The results reveal that the method is very effective, simple, and convenient. In addition, an error estimation of proposed method is presented.

机译：提出了一种基于搭配点的数值方法，通过泰勒矩阵方法求解非线性Klein-Gordon方程。将该方法应用于一些试验实例，并将数值结果与精确解进行比较。结果表明，该方法非常有效，简单，方便。另外，提出了所提出方法的误差估计。

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《Mathematical Problems in Engineering》 |2013年第7期|869749.1-869749.7|共7页
作者
Berna Buelbuel; Mehmet Sezer;
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作者单位

Department of Mathematics, Faculty of Science, Mugla University, 48000 Mugla, Turkey;

Department of Mathematics, Faculty of Science, Celal Bayar University, 45000 Manisa, Turkey;

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专利

1. Numerical solution of damped nonlinear Klein-Gordon equations using variational method and finite element approach [J] . Wang QF, Cheng DZ Applied mathematics and computation . 2005,第1期

机译：阻尼非线性Klein-Gordon方程的变分和有限元数值解
2. A spline collocation approach for the numerical solution of a generalized nonlinear Klein-Gordon equation [J] . Khuri SA, Sayfy A Applied mathematics and computation . 2010,第4期

机译：广义非线性Klein-Gordon方程数值解的样条配置方法
3. 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。
4. Numerical Solution of Nonlinear Klein-Gordon Equation Using Polynomial Wavelets [C] . Jalil Rashidinia, Mahmood Jokar International Conference on Applied Mathematics and Approximation Theory . 2016

机译：多项式小波非线性Klein-Gordon方程的数值解
5. Global Existence and Dispersion of Solutions to Nonlinear Klein-Gordon Equations with Potential. [D] . Wildman, Chad Thornton. 2014

机译：带电势的非线性Klein-Gordon方程解的整体存在和色散。
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. A remark on global solutions to nonlinear Klein-Gordon equation with a special quadratic nonlinearity in two space dimensions (Harmonic Analysis and Nonlinear Partial Differential Equations) [O] . Kato Jun, Ozawa Tohru 2009

机译：关于在二维空间上具有特殊二次非线性的非线性Klein-Gordon方程的整体解的注记（调和分析和非线性偏微分方程）

A New Approach to Numerical Solution of Nonlinear Klein-Gordon Equation

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