Introducing the stochastic Galerkin method in functions approximation depending on the random parameters

Authors: Khapisov M.Kh.
Published in issue: #3(98)/2025
DOI:
Category: Mathematics | Chapter: Computational Mathematics
Keywords: Hermite polynomials, polynomial chaos decomposition, stochastic Galerkin method, Simpson method, Cauchy problem, C++, Python
Published: 03.07.2025

The paper considers possibilities of applying the polynomial chaos concept in studying dynamic systems with the random parameters. It applies the intrusive stochastic Galerkin projection method in computing the coefficients to take into account in maximum the type of the linear differential operator describing the system. The method is implemented in the C++ and Python programming languages, numerical integration is performed with the Simpson method on the non-uniform mesh. The implemented algorithms efficiency is compared on the test functions. The method was applied to solving the problem of a linear damped oscillator, which was used to assess the approximation accuracy.

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