识别Rayleigh-Stokes方程源项的分数阶Landweber迭代正则化方法

该文研究具有Riemann-Liouville时间分数阶导数的Rayleigh-Stokes方程未知源识别问题.首先证明这个问题是不适定的,并应用分数阶Landweber正则化方法求解此反问题.基于条件稳定性结果,在先验和后验正则化参数选取规则下,分别给出精确解与正则解之间的误差估计.最后通过数值例子说明此方法求解此类反问题的有效性和可行性.

Numerical method of Rayleigh-Stokes problem for heated generalized second grade fluid with fractional derivative

In this paper,we consider the Rayleigh-Stokes problem for a heated generalized second grade fluid（RSP-HGSGF）with fractional derivative.An effective numerical method for approximating RSP-HGSGF in a bounded domain is presented.The stability and convergence of the method are analyzed.Numerical examples are presented to show the application of the present technique.