A comparative study to the numerical approximation of random Airy differential equation
The aim of this paper is twofold. First, we deal with the extension to the random framework of the piecewise Fröbenius method to solve Airy differential equations. This extension is based on mean square stochastic calculus. Second, we want to explore the capability to provide not only reliable appro...
| Autores: | , , , |
|---|---|
| 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:10251/37628 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/37628 |
| Access Level: | acceso abierto |
| Palabra clave: | Monte Carlo simulation Piecewise random Fröbenius method Polynomial chaos Random Airy-type differential equations Comparative studies Computational time Deterministic scenario Mean square Numerical approximations Numerical results Operational methods Oscillatory solutions Piece-wise Random differential equations Standard deviation Stochastic calculus Stochastic process Computer simulation Differential equations Monte Carlo methods Numerical methods Random processes Stochastic systems Differentiation (calculus) MATEMATICA APLICADA |
| Sumario: | The aim of this paper is twofold. First, we deal with the extension to the random framework of the piecewise Fröbenius method to solve Airy differential equations. This extension is based on mean square stochastic calculus. Second, we want to explore the capability to provide not only reliable approximations for both the average and the standard deviation functions associated to the solution stochastic process, but also to save computational time as it happens in dealing with the analogous problem in the deterministic scenario. This includes a comparison of the numerical results with respect to those obtained by other commonly used operational methods such as polynomial chaos and Monte Carlo simulations. To conduct this comparative study, we have chosen the Airy random differential equation because it has highly oscillatory solutions. This feature allows us to emphasize differences between all the considered approaches. © 2011 Elsevier Ltd. All rights reserved. |
|---|