多项时间-空间分数阶微分方程的PIM求解

PIM for Solving Multi-terms Time-space Fractional Equation

采用多项式基点插值(P IM)配置法求解多项时间-空间分数阶微分方程。首先进行时间离散得到半离散格式。然后,利用多项式基点插值离散空间变量得到全离散格式。最后,利用数值例子验证了数值方法的有效性。数值例子表明,无论是等距节点还是非等距节点,所提出的数值方法均能很好的近似微分方程的精确解。

In this paper, we make the first attempt to apply polynomial basis interpolation collocation method for the multi-terms time- space fractional equation. After diseretizing the time variable a senti-discrete scheme is obtained, then a full discrete scheme is proposed after diseretizing the space variable. Finally, the proposed numerical method is testified by numerical results with regular nodes and irreg- ular nodes.