Random Hermite differential equations: Mean square power series solutions and statistical properties
This paper deals with the construction of random power series solution of second order linear differential equations of Hermite containing uncertainty through its coefficients and initial conditions. Under appropriate hypotheses on the data, we establish that the constructed random power series solu...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/62895 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/62895 |
| Access Level: | acceso abierto |
| Palabra clave: | Mean square calculus Random differential equation Random Hermite polynomial Random power series solution Hermite Hermite differential equations Hermite polynomials Illustrative examples Initial conditions Mean square Monte Carlo Simulation Numerical results Power series solutions Random differential equations Random polynomials Second order linear differential equation Statistical functions Statistical properties Stochastic process Computer simulation Differential equations Monte Carlo methods Random processes Polynomials MATEMATICA APLICADA |
| Sumario: | This paper deals with the construction of random power series solution of second order linear differential equations of Hermite containing uncertainty through its coefficients and initial conditions. Under appropriate hypotheses on the data, we establish that the constructed random power series solution is mean square convergent. We provide conditions in order to obtain random polynomial solutions and, as a consequence, random Hermite polynomial are introduced. Also, the main statistical functions of the approximate stochastic process solution generated by truncation of the exact power series solution are given. Finally, we apply the proposed technique to several illustrative examples comparing the numerical results with respect to those provided by other available approaches including Monte Carlo simulation. © 2011 Elsevier Inc. All rights reserved. |
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