Análisis de un esquema de diferencias finitas para la solución numérica de una ecuación de convección difusión fraccionaria (2014)
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