03819nam 22007335 450 991098331580332120250915141622.09783031750236(electronic bk.)978303175022910.1007/978-3-031-75023-6(MiAaPQ)EBC31887331(Au-PeEL)EBL31887331(CKB)37345597800041(DE-He213)978-3-031-75023-6(OCoLC)1492991330(EXLCZ)993734559780004120250123d2025 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierNumerical Methods for Extreme Responses of Dynamical Systems Finite Dimensional Models /by Mircea D. Grigoriu1st ed. 2025.Cham :Springer Nature Switzerland :Imprint: Springer,2025.1 online resource (619 pages)Print version: Grigoriu, Mircea D. Numerical Methods for Extreme Responses of Dynamical Systems Cham : Springer,c2025 9783031750229 Introduction.-, Primer of probability theory -- , Random vectors and processes -- , Convergence of random elements -- , Extremes of random processes by finite dimensional (FD) models -- , Extremes of solutions of stochastic differential equations by finite dimensional (FD) models.This book constructs input finite dimensional (FD) models that are amendable for numerical calculations and provides accurate representations for responses of dynamical systems to these inputs, i.e., numerical solutions of stochastic equations. It establishes conditions under which numerical solutions of these equations deliver accurate estimates of extreme responses of dynamical systems that are needed to, for example, predict extreme weather events and design reliable aircrafts. It is intended to serve a broad audience including graduate students, researchers, engineers, scientists and applied mathematicians interested in the formulation and solutions of complex stochastic problems. Includes algorithms for constructing FD models for a broad range of inputs and generating realizations of these models; Uses data-based estimates of extremes of outputs of stochastic equations based on high/low fidelity numerical solutions; Gives practical criteria for the convergence of numerical estimates of extreme system responses.Stochastic analysisStochastic processesEngineering mathematicsEngineeringData processingStochastic AnalysisStochastic ProcessesStochastic Systems and ControlEngineering MathematicsMathematical and Computational Engineering ApplicationsAnàlisi estocàsticathubProcessos estocàsticsthubEnginyeriathubProcessament de dadesthubLlibres electrònicsthubStochastic analysis.Stochastic processes.Engineering mathematics.EngineeringData processing.Stochastic Analysis.Stochastic Processes.Stochastic Systems and Control.Engineering Mathematics.Mathematical and Computational Engineering Applications.Anàlisi estocàsticaProcessos estocàsticsEnginyeriaProcessament de dades519.22Grigoriu Mircea D148085MiAaPQMiAaPQMiAaPQ9910983315803321Numerical Methods for Extreme Responses of Dynamical Systems4316310UNINA