Numerical algorithm and computational experiments for one linear stochastic Hoff model

E. A. Soldatova   ; A. V. Keller

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 17 (2024) no. 2, pp. 83-95

Résumé

Investigated is a model of deformation in a structure composed of I-beams with random external effect; it is based on stochastic Hoff equations with an initial-final condition. The article describes an algorithm for a numerical solution of the initial-final problem for stochastic Hoff equations; the algorithm is based on the Galerkin method. Provided is a numerical investigation algorithm providing for numerical solutions for both degenerate and non-degenerate equations. The main theoretical results that enabled this numerical investigation are the methods of the theory of degenerate groups of operators and of the theory of the Sobolev type equations. The algorithms are represented by schemes enabling building flowcharts of programs for computational experiments. Results of computational experiments. In addition, numerical investigation of the stochastic model involves further obtaining and processing the results of $n$ experiments at various values of a random variable, including those related to rare events.

Détail

Keywords: Hoff model, geometric graph, initial-final condition, numerical investigation, algorithm, Sobolev type stochastic equations, computational experiment.

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