An implicit RBF meshless approach for solving the time fractional nonlinear sine-Gordon and Klein-Gordon equations
An implicit RBF meshless approach for solving the time fractional nonlinear sine-Gordon and Klein-Gordon equations
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DOI：
10.1016/j.enganabound.2014.09.008
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发表时间：
2015-01-01
影响因子：
3.3
通讯作者：
Mohebbi, Akbar
中科院分区：
文献类型：
--
作者：
Dehghan, Mehdi;Abbaszadeh, Mostafa;Mohebbi, Akbar
本文提出了一种求解时间分数阶非线性sine-Gordon方程的数值方法，该方程广泛存在于连续介质极限下的经典晶格动力学中，同时也是物理学中的Klein-Gordon方程。在这种方法中，我们首先通过O（tau（3-alpha），1 < alpha < 2）阶方案来近似所述方程的时间分数阶导数，然后我们将使用Kansa方法来近似空间导数。我们解决了这些方程的二维版本使用本文中提出的方法在不同的域，如矩形和非矩形域。证明了时间离散格式的无条件稳定性和收敛性。我们证明了时间离散格式的收敛阶为O（tau）。我们解决这些分数偏微分方程在不同的非矩形域。本文的目的是表明，基于径向基函数和配点法的无网格方法也适用于处理非线性时间分数阶偏微分方程。数值实验的结果与解析解进行了比较，以确认所提出的格式的精度和效率。(C)2014爱思唯尔有限公司版权所有。
In this paper, we propose a numerical method for the solution of time fractional nonlinear sine-Gordon equation that appears extensively in classical lattice dynamics in the continuum media limit and Klein-Gordon equation which arises in physics. In this method we first approximate the time fractional derivative of the mentioned equations by a scheme of order O(tau(3-alpha), 1 < alpha < 2 then we will use the Kansa approach to approximate the spatial derivatives. We solve the two-dimensional version of these equations using the method presented in this paper on different domains such as rectangular and non-rectangular domains. Also, we prove the unconditional stability and convergence of the time discrete scheme. We show that convergence order of the time discrete scheme is O(tau). We solve these fractional PDEs on different non-rectangular domains. The aim of this paper is to show that the meshless method based on the radial basis functions and collocation approach is also suitable for the treatment of the nonlinear time fractional PDEs. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme. (C) 2014 Elsevier Ltd. All rights reserved.