- -

Improving the approximation of the first and second order statistics of the response stochastic process to the random Legendre differential equation

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Improving the approximation of the first and second order statistics of the response stochastic process to the random Legendre differential equation

Mostrar el registro completo del ítem

Calatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2019). Improving the approximation of the first and second order statistics of the response stochastic process to the random Legendre differential equation. Mediterranean Journal of Mathematics. 16(3):1-14. https://doi.org/10.1007/s00009-019-1338-6

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/140202

Ficheros en el ítem

Thumbnail
Nombre: Calatayud-Gregori ...
Tamaño: 463.1Kb
Formato: PDF
Descripción: Versión del Autor.
Abrir/Preview
[Cerrado]
Nombre: Calatayud2019_Art ...
Tamaño: 416.0Kb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor

Metadatos del ítem

Título: Improving the approximation of the first and second order statistics of the response stochastic process to the random Legendre differential equation
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 deal with uncertainty quantification for the random Legendre differential equation, with input coefficient A and initial conditions X-0 and X-1. In a previous study (Calbo et al. in Comput Math Appl ...[+]
Palabras clave: Random Legendre differential equation , Random power series , Mean square calculus , Uncertainty quantification
Derechos de uso: Reserva de todos los derechos
Fuente:
Mediterranean Journal of Mathematics. (issn: 1660-5446 )
DOI: 10.1007/s00009-019-1338-6
Editorial:
Springer-Verlag
Versión del editor: https://doi.org/10.1007/s00009-019-1338-6
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/
Agradecimientos:
This work has been supported by the Spanish Ministerio de Economia y Competitividad Grant MTM2017-89664-P. Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo ...[+]
Tipo: Artículo

References

Soong, T.T.: Random Differential Equations in Science and Engineering. Academic Press, New York (1973)

Strand, J.L.: Random ordinary differential equations. J. Differ. Equ. 7(3), 538–553 (1970)

Smith, R.C.: Uncertainty quantification. Theory, implementation, and application. SIAM Comput. Sci. Eng. New York (2013) ISBN 9781611973211 [+]
Soong, T.T.: Random Differential Equations in Science and Engineering. Academic Press, New York (1973)

Strand, J.L.: Random ordinary differential equations. J. Differ. Equ. 7(3), 538–553 (1970)

Smith, R.C.: Uncertainty quantification. Theory, implementation, and application. SIAM Comput. Sci. Eng. New York (2013) ISBN 9781611973211

Fishman, G.: Monte Carlo: Concepts, Algorithms, and Applications. Springer, Berlin (2013)

Cortés, J.-C., Romero, J.-V., Roselló, M.-D., Santonja, F.-J., Villanueva, R.-J.: Solving continuous models with dependent uncertainty: a computational approach. Abstr. Appl. Anal. 2013, 983839 (2013). https://doi.org/10.1155/2013/983839

Xiu, D.: Numerical Methods for Stochastic Computations. A Spectral Method Approach. Cambridge Texts in Applied Mathematics. Princeton University Press, New York (2010)

El-Tawil, M.A.: The approximate solutions of some stochastic differential equations using transformations. Appl. Math. Comput. 164(1), 167–178 (2005)

Cortés, J.-C., Sevilla-Peris, P., Jódar, L.: Constructing approximate diffusion processes with uncertain data. Math. Comput. Simul. 73(1–4), 125–132 (2006)

Cortés, J.-C., Jódar, L., Villafuerte, L., Villanueva, R.-J.: Computing mean square approximations of random diffusion models with source term. Math. Comput. Simul. 76(1–3), 44–48 (2007)

Khodabin, M., Maleknejad, K., Rostami, M., Nouri, M.: Numerical solution of stochastic differential equations by second order Runge–Kutta methods. Math. Comput. Model. 53(9–10), 1910–1920 (2011)

Nouri, K., Ranjbar, H.: Mean square convergence of the numerical solution of random differential equations. Mediterran. J. Math. 12(3), 1123–1140 (2015)

Nouri, N.: Study on stochastic differential equations via modified Adomian decomposition method. U.P.B. Sci. Bull. Ser. A 78(1), 81–90 (2016)

Khodabin, M., Rostami, M.: Mean square numerical solution of stochastic differential equations by fourth order Runge–Kutta method and its application in the electric circuits with noise. Adv. Differ. Equ. 623, 1–19 (2015)

Díaz-Infante, S., Jerez, S.: Convergence and asymptotic stability of the explicit Steklov method for stochastic differential equations. J. Comput. Appl. Math. 291(1), 36–47 (2016)

Soheili, Ali R, Toutounian, F., Soleymani, F.: A fast convergent numerical method for matrix sign function with application in SDEs (Stochastic Differential Equations). J. Comput. Appl. Math. 282, 167–178 (2015)

Øksendal, B.: Stochastic Differential Equations. Springer, Berlin (2003)

Villafuerte, L., Braumann, C.A., Cortés, J.-C., Jódar, L.: Random differential operational calculus: theory and applications. Comput. Math. Appl. 59(1), 115–125 (2010)

Licea, J., Villafuerte, L., Chen-Charpentier, B.M.: Analytic and numerical solutions of a Riccati differential equation with random coefficients. J. Comput. Appl. Math. 309(1), 208–219 (2013)

Cortés, J.-C., Jódar, L., Camacho, J., Villafuerte, L.: Random Airy type differential equations: mean square exact and numerical solutions. Comput. Math. Appl. 60(5), 1237–1244 (2010)

Calbo, G., Cortés, J.-C., Jódar, L.: Random Hermite differential equations: mean square power series solutions and statistical properties. Appl. Math. Comput. 218(7), 3654–3666 (2011)

Calbo, G., Cortés, J.-C., Jódar, L., Villafuerte, L.: Solving the random Legendre differential equation: mean square power series solution and its statistical functions. Comput. Math. Appl. 61(9), 2782–2792 (2011)

Cortés, J.C., Jódar, L., Villafuerte, L.: Mean square solution of Bessel differential equation with uncertainties. J. Comput. Appl. Math. 309(1), 383–395 (2017)

Golmankhaneh, A.K., Porghoveh, N.A., Baleanu, D.: Mean square solutions of second-order random differential equations by using homotopy analysis method. Roman. Rep. Phys. 65(2), 350–362 (2013)

Khudair, A.K., Ameen, A.A., Khalaf, S.L.: Mean square solutions of second-order random differential equations by using Adomian decomposition method. Appl. Math. Sci. 51(5), 2521–2535 (2011)

Khudair, A.K., Haddad, S.A.M., Khalaf, S.L.: Mean square solutions of second-order random differential equations by using the differential transformation method. Open J. Appl. Sci. 6, 287–297 (2016)

Norman, L., Kotz, S., Balakrishnan, N.: Continuous Univariate Distributions, vol. 1. Wiley, Oxford (1994)

Ernst, O.G., Mugler, A., Starkloff, H.-J., Ullmann, E.: On the convergence of generalized polynomial chaos expansions. ESAIM Math. Modell. Num. Anal. 46(2), 317–339 (2012)

Shi, W., Zhang, C.: Error analysis of generalized polynomial chaos for nonlinear random ordinary differential equations. Appl. Num. Math. 62(12), 1954–1964 (2012)

Calatayud, J., Cortés, J.-C., Jornet, M.: On the convergence of adaptive gPC for non-linear random difference equations: theoretical analysis and some practical recommendations. J. Nonlinear Sci. Appl. 11(9), 1077–1084 (2018)

[-]

recommendations

 

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro completo del ítem