求解具有非线性源项的双侧空间分数阶扩散方程的样条方法

Spline approach for the two-side space fractional diffusion equation with a nonlinear source term

基于多项式样条函数,提出一种求解具有非线性源项的双侧空间分数阶扩散方程的数值方法.通过傅里叶分析证明了所提出的数值方法是无条件稳定和收敛的.为了验证所构造差分格式的有效性,引入分数阶行方法(MOL)与之进行比较.最后给出数值例子,并验证数值结果与理论分析是相吻合的.

In this paper,a numerical method based on the quadratic polynomial spline function is used to find the approximate solution for the two-side space fractional diffusion equation containing a nonlinear source term.The proposed method is proved to be unconditionally stable and convergent by Fourier analysis.For the purpose of evaluating the efficiency of the method,comparison with a fractional method of lines is made.Finally,some numerical examples are presented to show that numerical results agree satisfactorily with our theoretical analysis.