一类空间分数阶扩散方程系数反问题的数值解

The numerical solution of coefficient inverse problem for a kind of space fractional diffusion equation

数值求解一类空间分数阶扩散方程系数反问题。利用函数变换,将源项系数反问题转为对应的定解问题,并利用隐式差分格式求解,然后利用数值积分,求得待定系数函数的数值解,并且证明隐式差分格式的绝对稳定性。数值算例表明,该方法具有较高的精度。

The coefficient inversion for a kind of one-dimensional space fractional diffusion equation is concerned with numerical techniques. The coefficient inverse problem is converted to the corresponding definite problem through function transformation. Applying the implicit difference, the solution of the corresponding definite problem is founded. Using the numerical integral, the numerical solution of the undetermined function is obtained, and the unconditional stability of difference scheme is proved. The numerical example shows that the proposed method has high accuracy.