Modelo comparativo de la ecuación de calor unidimensional: perspectivas deterministas y estocásticas
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Resumo
Introducción: la incorporación de incertidumbre en los modelos de conducción de calor permite representar perturbaciones aleatorias presentes en diversos procesos físicos. Objetivos: la presente investigación se plantea como objetivo comparar las formulaciones determinista y estocástica de la ecuación del calor unidimensional bajo ruido blanco gaussiano aditivo y analizar la influencia de la difusividad térmica en la propagación de la incertidumbre. Metodología: se implementó una simulación computacional validada y reproducible para ecuaciones diferenciales parciales estocásticas en el software MATLAB, considerando un modelo determinista mediante esquema de Crank- Nicolson y una formulación estocástica mediante el método Euler-Maruyama. La incertidumbre se modeló con ruido blanco gaussiano aditivo y se evaluó mediante 200 simulaciones Monte Carlo en aluminio, acero inoxidable y madera. Se emplearon como métricas el RMSE, la varianza máxima y la energía térmica promedio. Resultados: la media del ensamblaje Monte Carlo presentó una elevada concordancia con la solución determinista. El incremento de la intensidad del ruido aumentó la dispersión estadística, mientras que la energía térmica promedio permaneció prácticamente constante. Conclusiones: en conclusión, la difusividad térmica actúa como un mecanismo natural de amortiguamiento de la incertidumbre, afectando principalmente la variabilidad de la solución sin modificar significativamente la dinámica promedio del proceso difusivo. Área de estudio general: Matemática Aplicada. Área de estudio específica: Simulación computacional. Tipo de estudio: Artículos originales.
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