Inverse Problem in Space Fractional Advection Diffusion Equation

Abstract

This work studies an inverse problem of determining the fractional order, a diffusion coefficient and the average velocity simultaneously in one-dimensional space fractional advection–diffusion equation. The forward problem is performed by an implicit finite difference scheme. Here, the solution of the inverse problem is performed in R environment using the Generalized Simulated Annealing algorithm (GenSA) package. Numerical experiments show that the algorithm is able to retrieve the parameters with good accuracy.