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Stochastic Ordinary And Stochastic Partial Differential Equations

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Stochastic Ordinary And Stochastic Partial Differential Equations

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Author : Peter Kotelenez
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-05

Stochastic Ordinary And Stochastic Partial Differential Equations written by Peter Kotelenez 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 2007-12-05 with Mathematics categories.

Stochastic Partial Differential Equations analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail. Coverage first describes the transition from the microscopic equations to the mesoscopic equations. It then covers a general system for the positions of the large particles.

Stochastic Ordinary And Stochastic Partial Differential Equations

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Author : Peter Kotelenez
language : en
Publisher: Springer
Release Date : 2008-11-01

Stochastic Ordinary And Stochastic Partial Differential Equations written by Peter Kotelenez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Mathematics categories.

Numerical Methods For Stochastic Partial Differential Equations With White Noise

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Author : Zhongqiang Zhang
language : en
Publisher: Springer
Release Date : 2017-09-01

Numerical Methods For Stochastic Partial Differential Equations With White Noise written by Zhongqiang Zhang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-01 with Mathematics categories.

This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made. Part III covers spatial white noise. Here the authors discuss numerical methods for nonlinear elliptic equations as well as other equations with additive noise. Numerical methods for SPDEs with multiplicative noise are also discussed using the Wiener chaos expansion method. In addition, some SPDEs driven by non-Gaussian white noise are discussed and some model reduction methods (based on Wick-Malliavin calculus) are presented for generalized polynomial chaos expansion methods. Powerful techniques are provided for solving stochastic partial differential equations. This book can be considered as self-contained. Necessary background knowledge is presented in the appendices. Basic knowledge of probability theory and stochastic calculus is presented in Appendix A. In Appendix B some semi-analytical methods for SPDEs are presented. In Appendix C an introduction to Gauss quadrature is provided. In Appendix D, all the conclusions which are needed for proofs are presented, and in Appendix E a method to compute the convergence rate empirically is included. In addition, the authors provide a thorough review of the topics, both theoretical and computational exercises in the book with practical discussion of the effectiveness of the methods. Supporting Matlab files are made available to help illustrate some of the concepts further. Bibliographic notes are included at the end of each chapter. This book serves as a reference for graduate students and researchers in the mathematical sciences who would like to understand state-of-the-art numerical methods for stochastic partial differential equations with white noise.

Control Of Partial Differential Equations

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Author : Jean-michel Coron
language : en
Publisher: World Scientific
Release Date : 2023-04-11

Control Of Partial Differential Equations written by Jean-michel Coron and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-11 with Mathematics categories.

This book is mainly a collection of lecture notes for the 2021 LIASFMA International Graduate School on Applied Mathematics. It provides the readers some important results on the theory, the methods, and the application in the field of 'Control of Partial Differential Equations'. It is useful for researchers and graduate students in mathematics or control theory, and for mathematicians or engineers with an interest in control systems governed by partial differential equations.

Random Perturbation Of Pdes And Fluid Dynamic Models

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Author : Franco Flandoli
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-11

Random Perturbation Of Pdes And Fluid Dynamic Models written by Franco Flandoli 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 2011-03-11 with Mathematics categories.

This volume explores the random perturbation of PDEs and fluid dynamic models. The text describes the role of additive and bilinear multiplicative noise, and includes examples of abstract parabolic evolution equations.

Advanced Topics In Computational Partial Differential Equations

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Author : Hans Petter Langtangen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-22

Advanced Topics In Computational Partial Differential Equations written by Hans Petter Langtangen 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 2012-09-22 with Mathematics categories.

This book is about solving partial differential equations (PDEs). Such equa tions are used to model a wide range ofphenomena in virtually all fields ofsci ence and technology. Inthe last decade, the general availability of extremely powerful computers has shifted the focus in computational mathematics from simplified model problems to much more sophisticated models resembling in tricate features of real life. This change challenges our knowledge in computer science and in numerical analysis. The main objective ofthe present book is to teach modern,advanced tech niques for numerical PDE solution. The book also introduces several models arising in fields likefinance, medicine, material technology, and geology. Inor der to read this book, you must have a basic knowledge of partial differential equations and numerical methods for solving such equations. Furthermore, some background in finite element methods is required. You do not need to know Diffpack, although this programming environment is used in examples throughout the text. Basically, this book is about models, methods, and how to implement the methods. For the implementation part it is natural for us to use Diffpack as the programming environment, because making a PDE solver in Diffpack requires little amount of programming and because Diff pack has support for the advanced numerical methods treated in this book. Most chapters have a part on models and methods, and a part on imple mentation and Diffpack programming. The exposition is designed such that readers can focus only on the first part, if desired.

Modern Stochastics And Applications

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Author : Volodymyr Korolyuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-30

Modern Stochastics And Applications written by Volodymyr Korolyuk 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 2014-01-30 with Mathematics categories.

This volume presents an extensive overview of all major modern trends in applications of probability and stochastic analysis. It will be a great source of inspiration for designing new algorithms, modeling procedures and experiments. Accessible to researchers, practitioners, as well as graduate and postgraduate students, this volume presents a variety of new tools, ideas and methodologies in the fields of optimization, physics, finance, probability, hydrodynamics, reliability, decision making, mathematical finance, mathematical physics and economics. Contributions to this Work include those of selected speakers from the international conference entitled “Modern Stochastics: Theory and Applications III,” held on September 10 –14, 2012 at Taras Shevchenko National University of Kyiv, Ukraine. The conference covered the following areas of research in probability theory and its applications: stochastic analysis, stochastic processes and fields, random matrices, optimization methods in probability, stochastic models of evolution systems, financial mathematics, risk processes and actuarial mathematics and information security.

Control And Inverse Problems For Partial Differential Equations

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Author : Gang Bao
language : en
Publisher: World Scientific
Release Date : 2019-04-03

Control And Inverse Problems For Partial Differential Equations written by Gang Bao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-03 with Mathematics categories.

This book is a collection of lecture notes for the LIASFMA Hangzhou Autumn School on 'Control and Inverse Problems for Partial Differential Equations' which was held during October 17-22, 2016 at Zhejiang University, Hangzhou, China. This autumn school is one of the activities organized by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA). Established jointly by eight institutions in China and France in 2014, LIASFMA aims at providing a platform for many leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in broad areas of applied mathematics.The book provides the readers with a unique and valuable opportunity to learn from and communicate with leading experts in control and inverse problems. And the readers are exposed not only to the basic theories and methods but also to the forefront of research directions in both fields.

Stochastic Partial Differential Equations Six Perspectives

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Author : René Carmona
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Stochastic Partial Differential Equations Six Perspectives written by René Carmona and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

Presents the main topics of interest in the field of stochastic partial differential equations (SPDEs), emphasizing breakthroughs and such basic issues as the role of SPDEs in stochastic modeling, how SPDEs arise, and how their theory is applied in different disciplines. Emphasis is placed on the genesis and applications of SPDEs, as well as mathematical theory and numerical methods. Suitable for graduate level students, researchers. Annotation copyrighted by Book News, Inc., Portland, OR

Stochastic Differential Equations

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Author : Peter H. Baxendale
language : en
Publisher: World Scientific
Release Date : 2007

Stochastic Differential Equations written by Peter H. Baxendale and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.

The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract attention of mathematicians of all generations, because, together with a short but thorough introduction to SPDEs, it presents a number of optimal and essentially non-improvable results about solvability for a large class of both linear and non-linear equations.

Stochastic Ordinary And Stochastic Partial Differential Equations

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