Solucion numérico-analítica de una ecuación de difusión bajo condiciones de incertidumbre utilizando DTM y Monte Carlo
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Keywords
modelos lineales de difusión aleatorios, condiciones de incertidumbre, Esquemas de diferencias finitas, método de transformación diferencial, solución analítica-numérica
Resumen
Un método numérico para resolver una ecuación parabólica general aleatoria lineal donde el coeficiente de difusión, el término fuente, las condiciones de contorno e iniciales incluyen la incertidumbre, se ha desarrollado. Ecuaciones de difusión surgen en muchos campos de la ciencia y la ingeniería, y en muchos casos, existen la incertidumbres debido a los datos que no se pueden saber, o debido a errores en las mediciones y la variabilidad intrínseca. Para modelar estas incertidumbres los parámetros correspondientes, coeficiente de difusión, término fuente, condiciones de contorno e iniciales, se suponen que son variables aleatorias con determinadas distribuciones de probabilidad. Basándose en los resultados numéricos, se obtienen los intervalos de confianza y valores medios esperados para la solución. Además, se obtienen con las soluciones numéricas-analíticas del método híbrido propuesto.
MSC: 35K10, 65C05, 65M99, 35R60
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Referencias
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