<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The main aim is to present recent developments in applications of symbolic computing in probabilistic and stochastic analysis, and this is done using the example of the well-known MAPLE system. The key theoretical methods discussed are (i) analytical derivations, (ii) the classical Monte-Carlo simulation approach, (iii) the stochastic perturbation technique, as well as (iv) some semi-analytical approaches. It is demonstrated in particular how to engage the basic symbolic tools implemented in any system to derive the basic equations for the stochastic perturbation technique and how to make an efficient implementation of the semi-analytical methods using an automatic differentiation and integration provided by the computer algebra program itself. The second important illustration is probabilistic extension of the finite element and finite difference methods coded in MAPLE, showing how to solve boundary value problems with random parameters in the environment of symbolic computing. The response function method belongs to the third group, where interference of classical deterministic software with the non-linear fitting numerical techniques available in various symbolic environments is displayed. We recover in this context the probabilistic structural response in engineering systems and show how to solve partial differential equations including Gaussian randomness in their coefficients.</p></abstract>

The main aim is to present recent developments in applications of symbolic computing in probabilistic and stochastic analysis, and this is done using the example of the well-known MAPLE system. The key theoretical methods discussed are (i) analytical derivations, (ii) the classical Monte-Carlo simulation approach, (iii) the stochastic perturbation technique, as well as (iv) some semi-analytical approaches. It is demonstrated in particular how to engage the basic symbolic tools implemented in any system to derive the basic equations for the stochastic perturbation technique and how to make an efficient implementation of the semi-analytical methods using an automatic differentiation and integration provided by the computer algebra program itself. The second important illustration is probabilistic extension of the finite element and finite difference methods coded in MAPLE, showing how to solve boundary value problems with random parameters in the environment of symbolic computing. The response function method belongs to the third group, where interference of classical deterministic software with the non-linear fitting numerical techniques available in various symbolic environments is displayed. We recover in this context the probabilistic structural response in engineering systems and show how to solve partial differential equations including Gaussian randomness in their coefficients.

Symbolic Computing in Probabilistic and Stochastic Analysis

Faculty of Civil Engineering, Architecture and Environmental Engineering, Łódź University of Technology, Al. Politechniki 6, 90-924 Łódź, Poland

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Symbolic Computing in Probabilistic and Stochastic Analysis"}

The main aim is to present recent developments in applications of symbolic computing in probabilistic and stochastic analysis, and this is done using the...

Symbolic Computing in Probabilistic and Stochastic Analysis

Pubblicato online: 30 dic 2015

Pagine: 961 - 973

Ricevuto: 17 ott 2013

DOI: https://doi.org/10.1515/amcs-2015-0069

Parole chiave
probabilistic analysis, stochastic computer methods, symbolic computation

© 2015 Marcin Kamiński, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Symbolic Computing in Probabilistic and Stochastic Analysis

Pubblicato online: 30 dic 2015

Pagine: 961 - 973

Ricevuto: 17 ott 2013

DOI: https://doi.org/10.1515/amcs-2015-0069

Parole chiaveprobabilistic analysis, stochastic computer methods, symbolic computation

© 2015 Marcin Kamiński, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Parole chiave
probabilistic analysis, stochastic computer methods, symbolic computation