{"id":{"repo_id":"unr","oai_identifier":"oai:scholarwolf.unr.edu:11714/2947"},"canonical_url":"https://search.dev.ndltd.org/etd/unr/oai:scholarwolf.unr.edu:11714/2947","repository":{"repo_id":"unr","name":"University of Nevada - Reno","base_url":"https://scholarwolf.unr.edu/server/oai/request"},"display":{"title":"A fast characteristic finite difference method for fractional advection-diffusion equations with non-linear reaction.","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["LaFleur, Anthony"],"institution":null,"degree_name":null,"degree_level":"Master's Degree","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Telyakovskiy, Aleksey S."],"committee_chairs":[],"committee_members":["Mortensen, Jeff W","Cooper, Clay"],"year":2014,"date_issued":"2014","date_published":"2014","updated_at":"2026-07-27T21:45:57Z","subjects":["Characteristic","Finite Difference","Fractional Calculus"],"languages":[],"rights":["In Copyright(All Rights Reserved)"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11714/2947","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Telyakovskiy, Aleksey S."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Mortensen, Jeff W","Cooper, Clay"]},{"key":"dc:creator","label":"Author","values":["LaFleur, Anthony"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-04-18T22:35:20Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2018-04-18T22:35:20Z"]},{"key":"dc:date.issued","label":"Date","values":["2014"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's Degree"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Characteristic","Finite Difference","Fractional Calculus"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright(All Rights Reserved)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11714/2947"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format","label":"Dc Format","values":["PDF"]},{"key":"dc:title","label":"Title","values":["A fast characteristic finite difference method for fractional advection-diffusion equations with non-linear reaction."]}]}],"canonical_facts":{"dc:contributor.advisor":["Telyakovskiy, Aleksey S."],"dc:contributor.committeemember":["Mortensen, Jeff W","Cooper, Clay"],"dc:creator":["LaFleur, Anthony"],"dc:date.accessioned":["2018-04-18T22:35:20Z"],"dc:date.available":["2018-04-18T22:35:20Z"],"dc:date.issued":["2014"],"dc:description.abstract":["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."],"dc:format":["PDF"],"dc:identifier.uri":["http://hdl.handle.net/11714/2947"],"dc:rights":["In Copyright(All Rights Reserved)"],"dc:subject":["Characteristic","Finite Difference","Fractional Calculus"],"dc:title":["A fast characteristic finite difference method for fractional advection-diffusion equations with non-linear reaction."],"dc:type":["Thesis"],"thesis:degree_level":["Master's Degree"]},"updated_at":"2026-07-27T21:45:57Z"}