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On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments

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On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments

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Calatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2019). On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments. Computational and Mathematical Methods. 1(4):1-12. https://doi.org/10.1002/cmm4.1045

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Metadatos del ítem

Título: On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments
Autor: Calatayud-Gregori, Julia Cortés, J.-C. Jornet-Sanz, Marc
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
[EN] In this paper, we construct two linearly independent response processes to the random Legendre differential equation on (-1,1)U(1,3), consisting of Lp(omega) convergent random power series around the regular¿singular ...[+]
Palabras clave: Lp random calculus , Random Legendre differential equation , Random power series , Regular-singular point , Uncertainty quantification
Derechos de uso: Reserva de todos los derechos
Fuente:
Computational and Mathematical Methods. (eissn: 2577-7408 )
DOI: 10.1002/cmm4.1045
Editorial:
John Wiley & Sons
Versión del editor: https://doi.org/10.1002/cmm4.1045
Código del Proyecto:
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-89664-P/ES/PROBLEMAS DINAMICOS CON INCERTIDUMBRE SIMULABLE: MODELIZACION MATEMATICA, ANALISIS, COMPUTACION Y APLICACIONES/
Descripción: "This is the peer reviewed version of the following article: Calatayud, J, Cortés, J-;C, Jornet, M. On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments. Comp and Math Methods. 2019; 1:e1045. https://doi.org/10.1002/cmm4.1045 , which has been published in final form at https://doi.org/10.1002/cmm4.1045. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."
Agradecimientos:
Spanish Ministerio de Economía y Competitividad, Grant/Award Number: MTM2017-89664-P; Programa de Ayudas de Investigación y Desarrollo; Universitat Politècnica de València
Tipo: Artículo

References

Calbo, G., Cortés, J.-C., Jódar, L., & Villafuerte, L. (2011). Solving the random Legendre differential equation: Mean square power series solution and its statistical functions. Computers & Mathematics with Applications, 61(9), 2782-2792. doi:10.1016/j.camwa.2011.03.045

Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061

Wong, E., & Hajek, B. (1985). Stochastic Processes in Engineering Systems. Springer Texts in Electrical Engineering. doi:10.1007/978-1-4612-5060-9 [+]
Calbo, G., Cortés, J.-C., Jódar, L., & Villafuerte, L. (2011). Solving the random Legendre differential equation: Mean square power series solution and its statistical functions. Computers & Mathematics with Applications, 61(9), 2782-2792. doi:10.1016/j.camwa.2011.03.045

Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061

Wong, E., & Hajek, B. (1985). Stochastic Processes in Engineering Systems. Springer Texts in Electrical Engineering. doi:10.1007/978-1-4612-5060-9

Nouri, K., & Ranjbar, H. (2014). Mean Square Convergence of the Numerical Solution of Random Differential Equations. Mediterranean Journal of Mathematics, 12(3), 1123-1140. doi:10.1007/s00009-014-0452-8

Lupulescu, V., O’Regan, D., & ur Rahman, G. (2014). Existence results for random fractional differential equations. Opuscula Mathematica, 34(4), 813. doi:10.7494/opmath.2014.34.4.813

Villafuerte, L., & Chen-Charpentier, B. M. (2012). A random differential transform method: Theory and applications. Applied Mathematics Letters, 25(10), 1490-1494. doi:10.1016/j.aml.2011.12.033

Licea, J. A., Villafuerte, L., & Chen-Charpentier, B. M. (2013). Analytic and numerical solutions of a Riccati differential equation with random coefficients. Journal of Computational and Applied Mathematics, 239, 208-219. doi:10.1016/j.cam.2012.09.040

Lang, S. (1997). Undergraduate Analysis. Undergraduate Texts in Mathematics. doi:10.1007/978-1-4757-2698-5

Cortés, J.-C., Romero, J.-V., Roselló, M.-D., Santonja, F.-J., & Villanueva, R.-J. (2013). Solving Continuous Models with Dependent Uncertainty: A Computational Approach. Abstract and Applied Analysis, 2013, 1-10. doi:10.1155/2013/983839

Calatayud, J., Cortés, J. C., Jornet, M., & Villanueva, R. J. (2018). Computational uncertainty quantification for random time-discrete epidemiological models using adaptive gPC. Mathematical Methods in the Applied Sciences, 41(18), 9618-9627. doi:10.1002/mma.5315

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