A novel numerical inverse technique for multi-parameter time fractional radially symmetric anomalous diffusion problem with initial singularity.

In this paper, the multi-parameter time fractional radially symmetric anomalous diffusion model used in porous media with initial singularity is considered. Both the direct numerical solution problem and the multi-parameter identification inverse problem are studied. Given the singularity in the initial time, a stable numerical scheme on nonuniform grid mesh is derived by using the L 2 − 1 σ method. To conduct the multi-parameter inversion problem, a novel hybrid Black Widow Optimization and Cuckoo Search (BWOCS) algorithm is proposed to combine the advantages of both the BWO algorithm and the CS algorithm, in order to improve the convergence speed and to achieve high-accuracy optimal results. Numerical examples are given to verify the efficiency and accuracy of the proposed numerical scheme and parameter inversion algorithm. Results show that the nonuniform grid L 2 − 1 σ scheme is efficient to deal with the time fractional radially symmetric anomalous diffusion problem with initial singularity, and the hybrid BWOCS algorithm has high precision and well convergence speed, compared with both the BWO and CS algorithms, which can be extended to other fractional inverse problems. [ABSTRACT FROM AUTHOR]