A fast characteristic finite difference method for fractional advection-diffusion equations with non-linear reaction
Posted on:2015-05-12
Degree:M.S
Type:Thesis
University:University of Nevada, Reno
Candidate:LaFleur, Anthony
Full Text:PDF
GTID:2470390020951298
Subject:Mathematics
Abstract/Summary:
Contaminant transport in porous media can be modeled with fractional differential equations. This approach results in early arrival of contaminants and heavy-tail distributions observed in field experiments. The implicit finite difference scheme with the shifted Grunwald approximation discritizing the fractional advection-diffusion equation unconditionally stable. We add an additional non-linear, Lipschitz continuous term to account for reactions and we solve the advection-diffusion equation utilizing fast Toeplitz matrix-vector multiplication. We then extend the method to the two-dimensional case. Numerical results are provided to compare performance of the methods proposed.