Numerical Procedures for Random Differential Equations
Some methodological approaches based on generalized polynomial chaos for linear differential equations with random parameters following various types of distribution laws are proposed. Mainly, an internal random coefficients method ‘IRCM’ is elaborated for a large number of random parameters. A proc...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2018/7403745 |
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| author | Mohamed Ben Said Lahcen Azrar Driss Sarsri |
| author_facet | Mohamed Ben Said Lahcen Azrar Driss Sarsri |
| author_sort | Mohamed Ben Said |
| collection | DOAJ |
| description | Some methodological approaches based on generalized polynomial chaos for linear differential equations with random parameters following various types of distribution laws are proposed. Mainly, an internal random coefficients method ‘IRCM’ is elaborated for a large number of random parameters. A procedure to build a new polynomial chaos basis and a connection between the one-dimensional and multidimensional polynomials are developed. This allows handling easily random parameters with various laws. A compact matrix formulation is given and the required matrices and scalar products are explicitly presented. For random excitations with an arbitrary number of uncertain variables, the IRCM is couplet to the superposition method leading to successive random differential equations with the same main random operator and right-hand sides depending only on one random parameter. This methodological approach leads to equations with a reduced number of random variables and thus to a large reduction of CPU time and memory required for the numerical solution. The conditional expectation method is also elaborated for reference solutions as well as the Monte-Carlo procedure. The applicability and effectiveness of the developed methods are demonstrated by some numerical examples. |
| format | Article |
| id | doaj-art-47f0769eba2d42be8248c08050b61a4b |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-47f0769eba2d42be8248c08050b61a4b2025-08-20T02:37:55ZengWileyJournal of Applied Mathematics1110-757X1687-00422018-01-01201810.1155/2018/74037457403745Numerical Procedures for Random Differential EquationsMohamed Ben Said0Lahcen Azrar1Driss Sarsri2Mathematical Modeling and Control, Department of Mathematics, Faculty of Sciences and Techniques of Tangier, Abdelmalek Essaadi University, Tangier, MoroccoResearch Center STIS, Department of Applied Mathematics and Informatics, ENSET, Mohammed V University, Rabat, MoroccoLTI, Ecole Nationale des Sciences Appliquées de Tanger, Abdelmalek Essaadi University, Tangier, MoroccoSome methodological approaches based on generalized polynomial chaos for linear differential equations with random parameters following various types of distribution laws are proposed. Mainly, an internal random coefficients method ‘IRCM’ is elaborated for a large number of random parameters. A procedure to build a new polynomial chaos basis and a connection between the one-dimensional and multidimensional polynomials are developed. This allows handling easily random parameters with various laws. A compact matrix formulation is given and the required matrices and scalar products are explicitly presented. For random excitations with an arbitrary number of uncertain variables, the IRCM is couplet to the superposition method leading to successive random differential equations with the same main random operator and right-hand sides depending only on one random parameter. This methodological approach leads to equations with a reduced number of random variables and thus to a large reduction of CPU time and memory required for the numerical solution. The conditional expectation method is also elaborated for reference solutions as well as the Monte-Carlo procedure. The applicability and effectiveness of the developed methods are demonstrated by some numerical examples.http://dx.doi.org/10.1155/2018/7403745 |
| spellingShingle | Mohamed Ben Said Lahcen Azrar Driss Sarsri Numerical Procedures for Random Differential Equations Journal of Applied Mathematics |
| title | Numerical Procedures for Random Differential Equations |
| title_full | Numerical Procedures for Random Differential Equations |
| title_fullStr | Numerical Procedures for Random Differential Equations |
| title_full_unstemmed | Numerical Procedures for Random Differential Equations |
| title_short | Numerical Procedures for Random Differential Equations |
| title_sort | numerical procedures for random differential equations |
| url | http://dx.doi.org/10.1155/2018/7403745 |
| work_keys_str_mv | AT mohamedbensaid numericalproceduresforrandomdifferentialequations AT lahcenazrar numericalproceduresforrandomdifferentialequations AT drisssarsri numericalproceduresforrandomdifferentialequations |