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Numerical Procedures for Random Differential Equations
Joint Authors
Sarsri, Driss
Ben Said, Mohamed
Azrar, Lahcen
Source
Journal of Applied Mathematics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-23, 23 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-05-21
Country of Publication
Egypt
No. of Pages
23
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Ben Said, Mohamed& Azrar, Lahcen& Sarsri, Driss. 2018. Numerical Procedures for Random Differential Equations. Journal of Applied Mathematics،Vol. 2018, no. 2018, pp.1-23.
https://search.emarefa.net/detail/BIM-1176042
Modern Language Association (MLA)
Ben Said, Mohamed…[et al.]. Numerical Procedures for Random Differential Equations. Journal of Applied Mathematics No. 2018 (2018), pp.1-23.
https://search.emarefa.net/detail/BIM-1176042
American Medical Association (AMA)
Ben Said, Mohamed& Azrar, Lahcen& Sarsri, Driss. Numerical Procedures for Random Differential Equations. Journal of Applied Mathematics. 2018. Vol. 2018, no. 2018, pp.1-23.
https://search.emarefa.net/detail/BIM-1176042
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1176042