A fast characteristic finite difference method for fractional advection-diffusion equations with non-linear reaction.

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.

Level thesis:degree_level

Master's Degree

Year dc:date.issued

2014

Author dc:creator

• LaFleur, Anthony

Advisor dc:contributor.advisor

• Telyakovskiy, Aleksey S.

Committee members dc:contributor.committeemember

• Mortensen, Jeff W
• Cooper, Clay

• Characteristic
• Finite Difference
• Fractional Calculus

Statement dc:rights

• In Copyright(All Rights Reserved)

Handle dc:identifier.uri

http://hdl.handle.net/11714/2947

OAI identifier oai:identifier

oai:scholarwolf.unr.edu:11714/2947