Symplectic Integration Of Stochastic Hamiltonian Systems

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Symplectic Integration Of Stochastic Hamiltonian Systems

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Author : Jialin Hong
language : en
Publisher: Springer Nature
Release Date : 2023-02-21

Symplectic Integration Of Stochastic Hamiltonian Systems written by Jialin Hong and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-21 with Mathematics categories.

This book provides an accessible overview concerning the stochastic numerical methods inheriting long-time dynamical behaviours of finite and infinite-dimensional stochastic Hamiltonian systems. The long-time dynamical behaviours under study involve symplectic structure, invariants, ergodicity and invariant measure. The emphasis is placed on the systematic construction and the probabilistic superiority of stochastic symplectic methods, which preserve the geometric structure of the stochastic flow of stochastic Hamiltonian systems. The problems considered in this book are related to several fascinating research hotspots: numerical analysis, stochastic analysis, ergodic theory, stochastic ordinary and partial differential equations, and rough path theory. This book will appeal to researchers who are interested in these topics.

Stochastic Numerics For Mathematical Physics

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Author : Grigori N. Milstein
language : en
Publisher: Springer Nature
Release Date : 2021-12-03

Stochastic Numerics For Mathematical Physics written by Grigori N. Milstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-03 with Computers categories.

This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.

Numerical Analysis And Its Applications

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Author : Ivan Dimov
language : en
Publisher: Springer
Release Date : 2013-10-01

Numerical Analysis And Its Applications written by Ivan Dimov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-01 with Computers categories.

This book constitutes thoroughly revised selected papers of the 5th International Conference on Numerical Analysis and Its Applications, NAA 2012, held in Lozenetz, Bulgaria, in June 2012. The 65 revised papers presented were carefully reviewed and selected from various submissions. The papers cover a broad area of topics of interest such as numerical approximation and computational geometry; numerical linear algebra and numerical solution of transcendental equation; numerical methods for differential equations; numerical stochastics, numerical modeling; and high performance scientific computing.

Numerical Approximation Of Ordinary Differential Problems

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Author : Raffaele D'Ambrosio
language : en
Publisher: Springer Nature
Release Date : 2023-09-26

Numerical Approximation Of Ordinary Differential Problems written by Raffaele D'Ambrosio and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-26 with Mathematics categories.

This book is focused on the numerical discretization of ordinary differential equations (ODEs), under several perspectives. The attention is first conveyed to providing accurate numerical solutions of deterministic problems. Then, the presentation moves to a more modern vision of numerical approximation, oriented to reproducing qualitative properties of the continuous problem along the discretized dynamics over long times. The book finally performs some steps in the direction of stochastic differential equations (SDEs), with the intention of offering useful tools to generalize the techniques introduced for the numerical approximation of ODEs to the stochastic case, as well as of presenting numerical issues natively introduced for SDEs. The book is the result of an intense teaching experience as well as of the research carried out in the last decade by the author. It is both intended for students and instructors: for the students, this book is comprehensive and rather self-contained; for the instructors, there is material for one or more monographic courses on ODEs and related topics. In this respect, the book can be followed in its designed path and includes motivational aspects, historical background, examples and a software programs, implemented in Matlab, that can be useful for the laboratory part of a course on numerical ODEs/SDEs. The book also contains the portraits of several pioneers in the numerical discretization of differential problems, useful to provide a framework to understand their contributes in the presented fields. Last, but not least, rigor joins readability in the book.

Numerical Approximations Of Stochastic Maxwell Equations

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Author : Chuchu Chen
language : en
Publisher: Springer Nature
Release Date : 2024-01-04

Numerical Approximations Of Stochastic Maxwell Equations written by Chuchu Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-04 with Mathematics categories.

The stochastic Maxwell equations play an essential role in many fields, including fluctuational electrodynamics, statistical radiophysics, integrated circuits, and stochastic inverse problems. This book provides some recent advances in the investigation of numerical approximations of the stochastic Maxwell equations via structure-preserving algorithms. It presents an accessible overview of the construction and analysis of structure-preserving algorithms with an emphasis on the preservation of geometric structures, physical properties, and asymptotic behaviors of the stochastic Maxwell equations. A friendly introduction to the simulation of the stochastic Maxwell equations with some structure-preserving algorithms is provided using MATLAB for the reader’s convenience. The objects considered in this book are related to several fascinating mathematical fields: numerical analysis, stochastic analysis, (multi-)symplectic geometry, large deviations principle, ergodic theory, partial differential equation, probability theory, etc. This book will appeal to researchers who are interested in these topics.

Invariant Measures For Stochastic Nonlinear Schr Dinger Equations

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Author : Jialin Hong
language : en
Publisher: Springer Nature
Release Date : 2019-08-22

Invariant Measures For Stochastic Nonlinear Schr Dinger Equations written by Jialin Hong and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-22 with Mathematics categories.

This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.

Explorations In Computational Physics

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Author : Devang Patil
language : en
Publisher: Educohack Press
Release Date : 2025-02-20

Explorations In Computational Physics written by Devang Patil and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.

"Explorations in Computational Physics" delves into the intricate world of computational physics, offering a comprehensive guide from fundamental theories to cutting-edge applications. This book serves as an indispensable companion for both novice learners and seasoned researchers. We cover a diverse array of topics, meticulously unfolding layers of computational techniques and their applications in various branches of physics. From classical mechanics simulations elucidating celestial mechanics to quantum mechanics computations unraveling atomic and subatomic realms, the book navigates through the vast landscape of computational methodologies with clarity and precision. Furthermore, we delve into electromagnetic field simulations, statistical mechanics, and thermodynamics, equipping readers with tools to model complex physical phenomena with accuracy and efficiency. High-performance computing techniques, data analysis, and visualization methodologies are elucidated, empowering readers to harness modern computational resources in their research. With lucid explanations, illustrative examples, and insightful discussions on emerging technologies like quantum computing and artificial intelligence, "Explorations in Computational Physics" fosters a deeper understanding of computational methodologies and their transformative impact on physics research.

Stochastic Structural Dynamics

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Author : Cho W. S. To
language : en
Publisher: John Wiley & Sons
Release Date : 2013-11-08

Stochastic Structural Dynamics written by Cho W. S. To and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-08 with Mathematics categories.

One of the first books to provide in-depth and systematic application of finite element methods to the field of stochastic structural dynamics The parallel developments of the Finite Element Methods in the 1950’s and the engineering applications of stochastic processes in the 1940’s provided a combined numerical analysis tool for the studies of dynamics of structures and structural systems under random loadings. In the open literature, there are books on statistical dynamics of structures and books on structural dynamics with chapters dealing with random response analysis. However, a systematic treatment of stochastic structural dynamics applying the finite element methods seems to be lacking. Aimed at advanced and specialist levels, the author presents and illustrates analytical and direct integration methods for analyzing the statistics of the response of structures to stochastic loads. The analysis methods are based on structural models represented via the Finite Element Method. In addition to linear problems the text also addresses nonlinear problems and non-stationary random excitation with systems having large spatially stochastic property variations. A systematic treatment of stochastic structural dynamics applying the finite element methods Highly illustrated throughout and aimed at advanced and specialist levels, it focuses on computational aspects instead of theory Emphasizes results mainly in the time domain with limited contents in the time-frequency domain Presents and illustrates direction integration methods for analyzing the statistics of the response of linear and nonlinear structures to stochastic loads Under Author Information - one change of word to existing text: He is a Fellow of the American Society of Mechanical Engineers (ASME)........

Handbook Of Differential Equations

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Author : Daniel Zwillinger
language : en
Publisher: Gulf Professional Publishing
Release Date : 1998

Handbook Of Differential Equations written by Daniel Zwillinger and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

This book compiles the most widely applicable methods for solving and approximating differential equations. as well as numerous examples showing the methods use. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations. For nearly every technique, the book provides: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users References to the literature for more discussion or more examples, including pointers to electronic resources, such as URLs

Numerical Integration Of Stochastic Differential Equations

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Author : G.N. Milstein
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-11-30

Numerical Integration Of Stochastic Differential Equations written by G.N. Milstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-30 with Computers categories.

This book is devoted to mean-square and weak approximations of solutions of stochastic differential equations (SDE). These approximations represent two fundamental aspects in the contemporary theory of SDE. Firstly, the construction of numerical methods for such systems is important as the solutions provided serve as characteristics for a number of mathematical physics problems. Secondly, the employment of probability representations together with a Monte Carlo method allows us to reduce the solution of complex multidimensional problems of mathematical physics to the integration of stochastic equations. Along with a general theory of numerical integrations of such systems, both in the mean-square and the weak sense, a number of concrete and sufficiently constructive numerical schemes are considered. Various applications and particularly the approximate calculation of Wiener integrals are also dealt with. This book is of interest to graduate students in the mathematical, physical and engineering sciences, and to specialists whose work involves differential equations, mathematical physics, numerical mathematics, the theory of random processes, estimation and control theory.