Symplectic Integration of Stochastic Hamiltonian Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symplectic Integration of Stochastic Hamiltonian Systems write by Jialin Hong. This book was released on 2023-02-21. Symplectic Integration of Stochastic Hamiltonian Systems available in PDF, EPUB and Kindle. 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
Stochastic Numerics for Mathematical Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Numerics for Mathematical Physics write by Grigori N. Milstein. This book was released on 2021-12-03. Stochastic Numerics for Mathematical Physics available in PDF, EPUB and Kindle. 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.
Symplectic Geometric Algorithms for Hamiltonian Systems
Symplectic Geometric Algorithms for Hamiltonian Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symplectic Geometric Algorithms for Hamiltonian Systems write by Kang Feng. This book was released on 2010-10-18. Symplectic Geometric Algorithms for Hamiltonian Systems available in PDF, EPUB and Kindle. "Symplectic Geometric Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development of numerical methodology for Hamiltonian systems is well motivated. Were it successful, it would imply wide-ranging applications.
Numerical Analysis and Its Applications
Numerical Analysis and Its Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Analysis and Its Applications write by Ivan Dimov. This book was released on 2013-10-01. Numerical Analysis and Its Applications available in PDF, EPUB and Kindle. 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
Numerical Approximation of Ordinary Differential Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Approximation of Ordinary Differential Problems write by Raffaele D'Ambrosio. This book was released on 2023-09-26. Numerical Approximation of Ordinary Differential Problems available in PDF, EPUB and Kindle. 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.
