Análisis de un esquema de diferencias finitas para la solución numérica de una ecuación de convección difusión fraccionaria
The nonlinear time fractional convection diffusion equation (TFCDE) is obtained from a standard nonlinear convection difusion equation by replacing the first-order time derivative with a fractional derivative (in Caputo sense) of order 2 (0; 1). Developing numerical methods for solving fractional pa...
- Autores:
-
Amador Rodriguez, Pedro Alejandro
- Tipo de recurso:
- Fecha de publicación:
- 2014
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/53646
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/53646
http://bdigital.unal.edu.co/48262/
- Palabra clave:
- 0 Generalidades / Computer science, information and general works
51 Matemáticas / Mathematics
derivada fraccional de caputo
Esquema de diferencias finito
Estabilidad
CFL
TVD
GUI
Caputo fractional derivative
Finite difference scheme
Stability
CFL
TVD
GUI
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | The nonlinear time fractional convection diffusion equation (TFCDE) is obtained from a standard nonlinear convection difusion equation by replacing the first-order time derivative with a fractional derivative (in Caputo sense) of order 2 (0; 1). Developing numerical methods for solving fractional partial differential equations is of increasing interest in many areas of Science and Engineering. In this thesis an explicit conservative finite difference scheme for TFCDE is introduced. We find its CFL condition and prove encouraging results regarding stability, namely, monotonicity, the TVD property and several bounds. Illustrative numerical examples are included in order to evaluate potential uses of the new method. Finally, we develop a graphical user interface (GUI) based in tool GUIDE of MATLAB for numerical solution TFCDE |
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