Numerical solution of a non-local fractional convection-diffusion equation

Authors

DOI:

https://doi.org/10.31908/19098367.2954

Keywords:

Finite Differences, Discrete Mollification, Fractional Derivation, Nonlocal Equation

Abstract

In this paper we consider a non-local time-fractional convection-diffusion equation. The fractional derivative is defined in the Caputo sense. The numerical solution is developed by an explicit numerical scheme using the finite differences method and discrete mollification for the non-local term.  From the numerical scheme and the von Neumann method, the stability condition (CFL) is established. The monotony property, the total variation property (TVD) and some important inequalities in the regularity of the scheme are proved using the stability condition. Finally, some numerical experiments with a source term are presented, which allows finding the analytical solutions to perform the respective calculations of the errors and convergence orders with the numerical approximation.

Author Biographies

  • Fernan Camilo Osorio Guzman, Universidad Católica de Pereira

    Profesor de la Universidad Católica de Pereira, profesional. Licenciado en Matemáticas y Física de la Universidad
    Tecnológica de Pereira, y Magister en Ciencias Matemáticas Aplicada de la Universidad Nacional de Colombia, Sede Manizales

  • Pedro Alejandro Amador Rodriguez, Universidad Nacional de Colombia

    Matemático y Magister en Ciencias Matemáticas Aplicada de la Universidad Nacional de Colombia, Sede Manizales. Áreas de estudio son los métodos numéricos en ecuaciones diferenciales parciales.

  • Carlos Andres Bedoya Parra, Fundación Universitaria Comfamiliar Risaralda

    Profesor de la Fundación Universitaria Comfamiliar Risaralda, Ingeniero Electricista y Magister Administración Económica y Financiera Física de la Universidad Tecnológica de Pereira.

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Published

2024-06-18

Issue

Vol. 18 No. 35 (2024)

Section

Artículos

How to Cite

Numerical solution of a non-local fractional convection-diffusion equation. (2024). Entre Ciencia E ingeniería, 18(35), 25-31. https://doi.org/10.31908/19098367.2954