- -

A mean square chain rule and its application in solving the random Chebyshev differential equation

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

A mean square chain rule and its application in solving the random Chebyshev differential equation

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: MJOM2016_chain_ru ...
Tamaño: 365.8Kb
Formato: PDF
Descripción: Versión del Autor.
Abrir
[Cerrado]
Nombre: Regla_Cadena_L2_M ...
Tamaño: 531.7Kb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor
dc.contributor.author Cortés, J.-C. es_ES
dc.contributor.author Villafuerte, Laura es_ES
dc.contributor.author Burgos-Simon, Clara es_ES
dc.date.accessioned 2018-07-16T06:56:40Z
dc.date.available 2018-07-16T06:56:40Z
dc.date.issued 2017 es_ES
dc.identifier.issn 1660-5446 es_ES
dc.identifier.uri http://hdl.handle.net/10251/105851
dc.description.abstract [EN] In this paper a new version of the chain rule for calculat- ing the mean square derivative of a second-order stochastic process is proven. This random operational calculus rule is applied to construct a rigorous mean square solution of the random Chebyshev differential equation (r.C.d.e.) assuming mild moment hypotheses on the random variables that appear as coefficients and initial conditions of the cor- responding initial value problem. Such solution is represented through a mean square random power series. Moreover, reliable approximations for the mean and standard deviation functions to the solution stochastic process of the r.C.d.e. are given. Several examples, that illustrate the theoretical results, are included. es_ES
dc.description.sponsorship This work was completed with the support of our TEX-pert.
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Mediterranean Journal of Mathematics es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Mean square chain rule es_ES
dc.subject Random Chebyshev differential equation es_ES
dc.subject Mean square and mean fourth calculus es_ES
dc.subject Monte Carlo simulations es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A mean square chain rule and its application in solving the random Chebyshev differential equation es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s00009-017-0853-6 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2013-41765-P/ES/METODOS COMPUTACIONALES PARA ECUACIONES DIFERENCIALES ALEATORIAS: TEORIA Y APLICACIONES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Instituto Universitario de Matemática Multidisciplinar - Institut Universitari de Matemàtica Multidisciplinària es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Cortés, J.; Villafuerte, L.; Burgos-Simon, C. (2017). A mean square chain rule and its application in solving the random Chebyshev differential equation. Mediterranean Journal of Mathematics. 14(1):14-35. https://doi.org/10.1007/s00009-017-0853-6 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.1007/s00009-017-0853-6 es_ES
dc.description.upvformatpinicio 14 es_ES
dc.description.upvformatpfin 35 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 14 es_ES
dc.description.issue 1 es_ES
dc.relation.pasarela S\337826 es_ES
dc.contributor.funder Ministerio de Economía, Industria y Competitividad es_ES
dc.description.references Calbo, G., Cortés, J.C., Jódar, L., Villafuerte, L.: Analytic stochastic process solutions of second-order random differential equations. Appl. Math. Lett. 23(12), 1421–1424 (2010). doi: 10.1016/j.aml.2010.07.011 es_ES
dc.description.references El-Tawil, M.A., El-Sohaly, M.: Mean square numerical methods for initial value random differential equations. Open J. Discret. Math. 1(1), 164–171 (2011). doi: 10.4236/ojdm.2011.12009 es_ES
dc.description.references Khodabin, M., Maleknejad, K., Rostami, K., Nouri, M.: Numerical solution of stochastic differential equations by second order Runge Kutta methods. Math. Comp. Model. 59(9–10), 1910–1920 (2010). doi: 10.1016/j.mcm.2011.01.018 es_ES
dc.description.references Santos, L.T., Dorini, F.A., Cunha, M.C.C.: The probability density function to the random linear transport equation. Appl. Math. Comput. 216(5), 1524–1530 (2010). doi: 10.1016/j.amc.2010.03.001 es_ES
dc.description.references González Parra, G., Chen-Charpentier, B.M., Arenas, A.J.: Polynomial Chaos for random fractional order differential equations. Appl. Math. Comput. 226(1), 123–130 (2014). doi: 10.1016/j.amc.2013.10.51 es_ES
dc.description.references El-Beltagy, M.A., El-Tawil, M.A.: Toward a solution of a class of non-linear stochastic perturbed PDEs using automated WHEP algorithm. Appl. Math. Model. 37(12–13), 7174–7192 (2013). doi: 10.1016/j.apm.2013.01.038 es_ES
dc.description.references Nouri, K., Ranjbar, H.: Mean square convergence of the numerical solution of random differential equations. Mediterran. J. Math. 12(3), 1123–1140 (2015). doi: 10.1007/s00009-014-0452-8 es_ES
dc.description.references Villafuerte, L., Braumann, C.A., Cortés, J.C., Jódar, L.: Random differential operational calculus: theory and applications. Comp. Math. Appl. 59(1), 115–125 (2010). doi: 10.1016/j.camwa.2009.08.061 es_ES
dc.description.references Øksendal, B.: Stochastic differential equations: an introduction with applications, 6th edn. Springer, Berlin (2007) es_ES
dc.description.references Soong, T.T.: Random differential equations in science and engineering. Academic Press, New York (1973) es_ES
dc.description.references Wong, B., Hajek, B.: Stochastic processes in engineering systems. Springer Verlag, New York (1985) es_ES
dc.description.references Arnold, L.: Stochastic differential equations. Theory and applications. John Wiley, New York (1974) es_ES
dc.description.references 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). doi: 10.1016/j.camwa.2010.05.046 es_ES
dc.description.references Calbo, G., Cortés, J.C., Jódar, L.: Random Hermite differential equations: mean square power series solutions and statistical properties. Appl. Math. Comp. 218(7), 3654–3666 (2011). doi: 10.1016/j.amc.2011.09.008 es_ES
dc.description.references Calbo, G., Cortés, J.C., Jódar, L., Villafuerte, L.: Solving the random Legendre differential equation: Mean square power series solution and its statistical functions. Comp. Math. Appl. 61(9), 2782–2792 (2010). doi: 10.1016/j.camwa.2011.03.045 es_ES
dc.description.references Cortés, J.C., Jódar, L., Company, R., Villafuerte, L.: Laguerre random polynomials: definition, differential and statistical properties. Utilit. Math. 98, 283–293 (2015) es_ES
dc.description.references Cortés, J.C., Jódar, L., Villafuerte, L.: Mean square solution of Bessel differential equation with uncertainties. J. Comp. Appl. Math. 309, 383–395 (2017). doi: 10.1016/j.cam.2016.01.034 es_ES
dc.description.references Golmankhaneh, A.K., Porghoveh, N.A., Baleanu, D.: Mean square solutions of second-order random differential equations by using homotopy analysis method. Romanian Reports Physics 65(2), 1237–1244 (2013) es_ES
dc.description.references Khalaf, S.L.: Mean square solutions of second-order random differential equations by using homotopy perturbation method. Int. Math. Forum 6(48), 2361–2370 (2011) es_ES
dc.description.references Khudair, A.R., Ameen, A.A., Khalaf, S.L.: Mean square solutions of second-order random differential equations by using Adomian decomposition method. Appl. Math. Sci. 5(49), 2521–2535 (2011) es_ES
dc.description.references Agarwal, R.P., O’Regan, D.: Ordinary and partial differential equations. Springer, New York (2009) es_ES


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

Mostrar el registro sencillo del ítem