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

作　　者：阮周生[1,2] 张文[1,2] 王泽文[2] 

机构地区：[1]东华理工大学放射性地质与勘探技术国防重点学科实验室,南昌330013 [2]东华理工大学理学院,南昌330013

出　　处：《黑龙江大学自然科学学报》2012年第6期759-763,共5页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(41001320;11161002);江西省自然科学基金资助项目(2009GZS0001);江西省教育厅科学技术研究项目(GJJ11151);放射性地质与勘探技术国防重点学科实验室项目(2010RGET12)

摘　　要：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.

关 键 词：反常扩散 空间分数阶导数 反问题 有限差分格式 稳定性 

分 类 号：O175.29[理学—数学]