Solution of a time fractional inverse advection-dispersion problem by discrete mollification

ABSTRACT: We consider an inverse problem for a time fractional advection-dispersion equation in a 1-D semi-infinite setting. The fractional derivative is interpreted in the sense of Caputo and advection and dispersion coefficients are constant. The inverse problem consists on the recovery of the boundary distribution of solute concentration and dispersion flux from measured (noisy) data known at an interior location. This inverse problem is ill-posed and thus the numerical solution must include some regularization technique. Our approach is a finite difference space marching scheme enhanced by adaptive discrete mollification. Error estimates and illustrative numerical examples are provided.

• Autores: Mejía, Carlos; Piedrahita Monroy, Julian Alejandro
• Tipo de recurso: Article of investigation
• Fecha de publicación: 2017
• Institución: Universidad de Antioquia
• Repositorio: Repositorio UdeA
• Idioma: eng
• OAI Identifier: oai:bibliotecadigital.udea.edu.co:10495/29203
• Acceso en línea: http://hdl.handle.net/10495/29203; http://www.scielo.org.co/scielo.php?pid=S0034-74262017000100083&script=sci_abstract&tlng=en
• Palabra clave: Derivadas (Matemáticas); Diferencias finitas; Finite Differences; Derivadas fraccionales
• Rights: openAccess
• License: http://creativecommons.org/licenses/by/2.5/co/