Solución Numérica de una ecuación de convección-difusión no local fraccionaria
Resumen
En este artículo se considera una ecuación de convección-difusión no local fraccionaria en el tiempo. La derivada fraccional se define en el sentido de Caputo, y las soluciones numéricas se desarrollan por medio de un esquema numérico explícito usando el método de diferencias finitas y la molificación discreta para el término no local. A partir del esquema numérico y el método de Von Neumann se establece la condición de estabilidad (CFL), la propiedad de monotonía, la propiedad de variación total (TVD) y algunas desigualdades importantes para la regularidad del esquema. Finalmente, se presenta algunos experimentos numéricos con un término fuente, el cual permite encontrar las soluciones analíticas para realizar los cálculos respectivos de los errores y órdenes de convergencia con la aproximación numérica.
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