多项分数阶非线性波动方程的数值方法及其快速实现

对带有空间四阶导数的多项时间分数阶非线性波动方程构造了一个线性化数值方法. 该方法采用线性化技术离散非线性项,从而避免求非线性方程组,并严格地证明了该方法的收敛性,在时间方向具有一阶精度,在空间方向具有四阶精度.该方法同样适用于初始奇异性问题,并且还可以用指数和技术来进行快速实现. 最后,通过数值实验验证了该方法的有效性和理论分析的正确性.

A numerical method and its fast implementation for multi-term fractional nonlinear wave equations

A linearized numerical method for multi-term time fractional nonlinear wave equations with a spatial fourth-order derivative is derived. To avoid solving the nonlinear system of equations, a linearized technique is applied to discretize the nonlinear term. Then, the convergence of this presented method is rigorously proved with the first-order accuracy in time and the fourth-order accuracy in space. It is worth mentioning that the presented method can handle the initial singularity, and can be fast calculated by the sum-of-exponentials technique. Finally, numerical experiments are given to verify the effectiveness of this method and the correctness of the theoretical results.