International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

Probabilistic analysis of a foundational class of generalized second-order linear differential equations in classic mechanics

A number of relevant models in Classical Mechanics are formulated by means of the differential equation y′′(t)+Atβy(t)=0 . In this paper, we improve the results recently established for a randomized reformulation of this model that includes a generalized derivative. The stochastic analysis permits solving that generalized model by computing reliable approximations of the probability density function of the solution, which is a stochastic process. The approach avoids constructing these approximations from limited statistical punctual information and the Principle of Maximum Entropy by directly constructing a sequence of approximations using the Probabilistic Transformation Method. We prove that these approximations converge to the exact density under mild conditions on the data. Finally, several numerical examples illustrate our theoretical findings.This paper has been supported by the grant PID2020–115270GB–I00 funded by MCIN/AEI/10.13039/501100011033 and by the grant AICO/2021/302 (Generalitat Valenciana). The author CP was partially supported by CMUP (UID/-MAT/00144/2013), which is funded by Fundação para a Ciência e Tecnologia (FCT) (Portugal) with national (MEC) and European structural funds European Regional Development Fund (FEDER), under the partnership agreement PT2020.info:eu-repo/semantics/publishedVersio