中文摘要：

数值求解一类空间分数阶扩散方程源项系数反问题.利用函数变换,将源项系数反问题转为对应的定解问题,利用隐式差分格式,求解对应定解问题,然后利用数值积分,求得待定系数函数的数值解,并且证明了隐式差分格式的绝对稳定性.通过数值算例表明,该数值方法具有较高的计算精度.

英文摘要：

A numerical method for source coefficient inverse problem of a kind of one-dimensional space fractional diffusion equation is concerned.The inverse problem of source coefficient 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 founded,and the unconditional stability of difference scheme is proved.The numerical example shows that the proposed method has high accuracy.