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Number 4 - December 2015
Volume 25 - 2015
Symbolic computing in probabilistic and stochastic analysis
Marcin Kamiński
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.
Keywords
probabilistic analysis, stochastic computer methods, symbolic computation