Solving Continuous Models with Dependent Uncertainty: A Computational Approach
This paper presents a computational study on a quasi-Galerkin projection-based method to deal with a class of systems of random ordinary differential equations (r.o.d.e.’s) which is assumed to depend on a finite number of random variables (r.v.’s). This class of systems of r.o.d.e.’s appears in diff...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/983839 |
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| author | J.-C. Cortés J.-V. Romero M.-D. Roselló Francisco-J. Santonja Rafael-J. Villanueva |
| author_facet | J.-C. Cortés J.-V. Romero M.-D. Roselló Francisco-J. Santonja Rafael-J. Villanueva |
| author_sort | J.-C. Cortés |
| collection | DOAJ |
| description | This paper presents a computational study on a quasi-Galerkin projection-based method to deal with a class of systems of random ordinary differential equations (r.o.d.e.’s) which is assumed to depend on a finite number of random variables (r.v.’s). This class of systems of r.o.d.e.’s appears in different areas, particularly in epidemiology modelling. In contrast with the other available Galerkin-based techniques, such as the generalized Polynomial Chaos, the proposed method expands the solution directly in terms of the random inputs rather than auxiliary r.v.’s. Theoretically, Galerkin projection-based methods take advantage of orthogonality with the aim of simplifying the involved computations when solving r.o.d.e.’s, which means to compute both the solution and its main statistical functions such as the expectation and the standard deviation. This approach requires the previous determination of an orthonormal basis which, in practice, could become computationally burden and, as a consequence, could ruin the method. Motivated by this fact, we present a technique to deal with r.o.d.e.’s that avoids constructing an orthogonal basis and keeps computationally competitive even assuming statistical dependence among the random input parameters. Through a wide range of examples, including a classical epidemiologic model, we show the ability of the method to solve r.o.d.e.’s. |
| format | Article |
| id | doaj-art-d3c9fbc403b1428ca204709bd2cd9183 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d3c9fbc403b1428ca204709bd2cd91832025-08-20T03:24:12ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/983839983839Solving Continuous Models with Dependent Uncertainty: A Computational ApproachJ.-C. Cortés0J.-V. Romero1M.-D. Roselló2Francisco-J. Santonja3Rafael-J. Villanueva4Instituto Universitario de Matemática Multidisciplinar, Building 8G, 2nd Floor Access C, Universitat Politècnica de València, 46022 Valencia, SpainInstituto Universitario de Matemática Multidisciplinar, Building 8G, 2nd Floor Access C, Universitat Politècnica de València, 46022 Valencia, SpainInstituto Universitario de Matemática Multidisciplinar, Building 8G, 2nd Floor Access C, Universitat Politècnica de València, 46022 Valencia, SpainDepartamento de Estadística e Investigación Operativa, Facultad de Ciencias Matemáticas, Universitat de València, Avenida Doctor Moliner S/N, Burjassot, 46100 Valencia, SpainInstituto Universitario de Matemática Multidisciplinar, Building 8G, 2nd Floor Access C, Universitat Politècnica de València, 46022 Valencia, SpainThis paper presents a computational study on a quasi-Galerkin projection-based method to deal with a class of systems of random ordinary differential equations (r.o.d.e.’s) which is assumed to depend on a finite number of random variables (r.v.’s). This class of systems of r.o.d.e.’s appears in different areas, particularly in epidemiology modelling. In contrast with the other available Galerkin-based techniques, such as the generalized Polynomial Chaos, the proposed method expands the solution directly in terms of the random inputs rather than auxiliary r.v.’s. Theoretically, Galerkin projection-based methods take advantage of orthogonality with the aim of simplifying the involved computations when solving r.o.d.e.’s, which means to compute both the solution and its main statistical functions such as the expectation and the standard deviation. This approach requires the previous determination of an orthonormal basis which, in practice, could become computationally burden and, as a consequence, could ruin the method. Motivated by this fact, we present a technique to deal with r.o.d.e.’s that avoids constructing an orthogonal basis and keeps computationally competitive even assuming statistical dependence among the random input parameters. Through a wide range of examples, including a classical epidemiologic model, we show the ability of the method to solve r.o.d.e.’s.http://dx.doi.org/10.1155/2013/983839 |
| spellingShingle | J.-C. Cortés J.-V. Romero M.-D. Roselló Francisco-J. Santonja Rafael-J. Villanueva Solving Continuous Models with Dependent Uncertainty: A Computational Approach Abstract and Applied Analysis |
| title | Solving Continuous Models with Dependent Uncertainty: A Computational Approach |
| title_full | Solving Continuous Models with Dependent Uncertainty: A Computational Approach |
| title_fullStr | Solving Continuous Models with Dependent Uncertainty: A Computational Approach |
| title_full_unstemmed | Solving Continuous Models with Dependent Uncertainty: A Computational Approach |
| title_short | Solving Continuous Models with Dependent Uncertainty: A Computational Approach |
| title_sort | solving continuous models with dependent uncertainty a computational approach |
| url | http://dx.doi.org/10.1155/2013/983839 |
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