A Runge-Kutta Gegenbauer spectral method for nonlinear fractional differential equations with Riesz fractional derivatives
A Runge-Kutta Gegenbauer spectral method for nonlinear fractional differential equations with Riesz fractional derivatives
复制标题
具有Riesz分数阶导数的非线性分数阶微分方程的Runge-Kutta Gegenbauer谱方法
DOI：
10.1080/00207160.2018.1487059
复制
发表时间：
2019
影响因子：
1.8
通讯作者：
Qu Haidong
中科院分区：
文献类型：
--
作者：
Lin Fu-Rong;Qu Haidong
提出了一种Runge-Kutta Gegenbauer谱方法来求解一类二维变系数分数阶非线性微分方程的初边值问题。在每一个时间步的问题的解决方案是由一个二元多项式的基础上移位Gegenbauer多项式近似，然后三阶龙格库塔方法应用于该问题。分析了该方法的收敛速度。数值结果验证了该方法的有效性。
A Runge–Kutta Gegenbauer spectral method is proposed to solve an initial-boundary value problem for a nonlinear two-dimensional fractional differential equation with variable coefficients. The solution to the problem at each time step is approximated by a bivariate polynomial based on shifted Gegenbauer polynomials and then the Runge–Kutta method of order 3 is applied to the problem. The convergence rate of the derived method is analysed. Numerical results are presented to verify the effectiveness of the method.