分数阶电报方程一类有效的普遍性差分方法

A Kind of Efficient Universal Differential Methods for Fractional Telegraph Equations

摘要: 对时间分数阶电报方程构造了一类普遍性差分方法，采用傅里叶方法分析该类差分方法的稳定性和收敛性；最后，通过数值试验验证本文方法求解分数阶电报方程的有效性。选取不同θ值进行比较分析，数值结果表明当θ取0.5附近时，数值解的精度较好；表明普遍性差分方法求解时间分数阶电报方程是有效的。

Abstract: A kind of universal difference method is constructed for the time fractional telegraph equation. The stability and convergence of the difference method are analyzed by Fourier method. Finally, the effectiveness of the method for solving the fractional telegraph equation is verified by numerical experiments. The comparison of different θ values is carried out. The numerical results show that the numerical solution is better when θ is around 0.5. Therefore, it is effective to solve the time-fractional telegraph equation by the universal difference method.