Método de Tau Aplicado a un Problema de Stefan a Dos Fases con Coeficientes Térmicos Variables
DOI:
https://doi.org/10.70567/mc.v41i15.78Palavras-chave:
Coeficientes térmicos variables, problema de Stefan, solución de tipo similaridad, método de TauResumo
Se considera un problema de Stefan a dos fases para un material semi-infinito con coeficientes térmicos variables, dependientes de una potencia de la temperatura. Mediante la transformación de similaridad, se obtiene un problema diferencial ordinario equivalente. Por un lado, se prueba la existencia y unicidad de solución, imponiendo una condición de Dirichlet en el borde fijo. Por otra parte, se obtienen soluciones aproximadas mediante el método de Tau, basado en la matriz operacional de las derivadas de los poliniomios de Chebyshev. Para el caso particular que surge cuando se consideran coeficientes térmicos constantes, se compara la solución exacta disponible en la literatura con las aproximaciones obtenidas con el fin de testear la exactitud del método de aproximación empleado.
Referências
Abdelhamied D., Abdelhakem M., El-Kady M., y Youssri M. Adapted Shifted ChebyshevU Operational Matrix of Derivates: Two Algorithms for Solving Even-Order BVPs. Applied Mathematics and Information, 17(3):575-581, 2023. https://doi.org/10.18576/amis/170318
AliAbadi M. y Ortiz E. Numerical treatment of moving and free boundary value problems with the tau method. Computers and Mathematics with Applications, 35(8):53 - 61, 1998. https://doi.org/10.1016/S0898-1221(98)00044-3
Bollati J., Natale M.F., Semitiel J.A., y Tarzia D.A. A two-phase Stefan problem with powertype temperature-dependent thermal conductivity. Existence of a solution by two fixed points and numerical results. AIMS Mathematics, 9:21189-21211, 2024. https://doi.org/10.3934/math.20241029
Bougoffa L., Bougouffa S., y Khanfer A. An Analysis of the One-Phase Stefan Problem with Variable Thermal Coefficients of Order p. Axioms, 12, 2023. https://doi.org/10.3390/axioms12050497
Hesameddini E. y Riahi M. Shifted Chebyshev polynomial method for solving systems of linear and nonlinear Fredhom-Volterra integro-differential equations. Journal of Mathematical Extension, 12(3):55-79, 2018.
Kumar A., Singh A.K., y Rajeev R. A Stefan problem with variable thermal coefficients and moving phase change material. Journal of King Saud University Science, 31:1064-1069, 2019. https://doi.org/10.1016/j.jksus.2018.09.009
Kumar A., Singh A.K., y Rajeev R. A moving boundary problem with variable specific heat and thermal conductivity. Journal of King Saud University - Science, 32:384-389, 2020. https://doi.org/10.1016/j.jksus.2018.05.028
Lanczos C. Trigonometric interpolation of empirical and analytical functions. Studies in Applied Mathematics, 17(1-4):123 - 199, 1938. doi:10.1002/sapm1938171123. https://doi.org/10.1002/sapm1938171123
Ortiz E.L. The tau method. SIAM Journal on Numerical Analysis, 6(3):480-492, 1969. https://doi.org/10.1137/0706044
Raslan K., Ali K., Mohamed E., Younis J., y Abd El salam M. An Operational Matrix Technique Based on Chebyshev Polynomials for Solving Mixed Volterra-Fredholm Delay Integro-Differential Equations of Variable-Order. Journal of Function Spaces, 2022(6203440):1-15, 2022. https://doi.org/10.1155/2022/6203440
Sahlan M. y Feyzollahzadeh H. Operational matrices of Chebyshev polynomials for solving singular Volterra integral equations. Mathematical Sciences, 11:165-171, 2017. https://doi.org/10.1007/s40096-017-0222-4
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