Random Ordinary Differential Equations And Their Numerical Solution

Author : Xiaoying Han
Publisher : Springer
ISBN 13 : 981106265X
Total Pages : 250 pages
Book Rating : 4.50/5 ( download)

DOWNLOAD NOW!

Download or read book Random Ordinary Differential Equations and Their Numerical Solution written by Xiaoying Han and published by Springer. This book was released on 2017-10-25 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs). RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems. They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor expansions in the usual sense. However, Taylor-like expansions can be derived for RODEs using an iterated application of the appropriate chain rule in integral form, and represent the starting point for the systematic derivation of consistent higher order numerical schemes for RODEs. The book is directed at a wide range of readers in applied and computational mathematics and related areas as well as readers who are interested in the applications of mathematical models involving random effects, in particular in the biological sciences.The level of this book is suitable for graduate students in applied mathematics and related areas, computational sciences and systems biology. A basic knowledge of ordinary differential equations and numerical analysis is required.

Author : S. S. Artemiev
Publisher : Walter de Gruyter
ISBN 13 : 3110944669
Total Pages : 185 pages
Book Rating : 4.62/5 ( download)

DOWNLOAD NOW!

Download or read book Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations written by S. S. Artemiev and published by Walter de Gruyter. This book was released on 2011-02-11 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text deals with numerical analysis of systems of both ordinary and stochastic differential equations. It covers numerical solution problems of the Cauchy problem for stiff ordinary differential equations (ODE) systems by Rosenbrock-type methods (RTMs).

Author : L.F. Shampine
Publisher : Routledge
ISBN 13 : 1351427555
Total Pages : 632 pages
Book Rating : 4.55/5 ( download)

DOWNLOAD NOW!

Download or read book Numerical Solution of Ordinary Differential Equations written by L.F. Shampine and published by Routledge. This book was released on 2018-10-24 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new work is an introduction to the numerical solution of the initial value problem for a system of ordinary differential equations. The first three chapters are general in nature, and chapters 4 through 8 derive the basic numerical methods, prove their convergence, study their stability and consider how to implement them effectively. The book focuses on the most important methods in practice and develops them fully, uses examples throughout, and emphasizes practical problem-solving methods.

Author : Peter E. Kloeden
Publisher : Springer Science & Business Media
ISBN 13 : 3662126168
Total Pages : 666 pages
Book Rating : 4.65/5 ( download)

DOWNLOAD NOW!

Download or read book Numerical Solution of Stochastic Differential Equations written by Peter E. Kloeden and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP

Author : Uri M. Ascher
Publisher : SIAM
ISBN 13 : 0898713544
Total Pages : 617 pages
Book Rating : 4.41/5 ( download)

DOWNLOAD NOW!

Download or read book Numerical Solution of Boundary Value Problems for Ordinary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 1988-01-01 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.

Author : Douglas Quinney
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.72/5 ( download)

DOWNLOAD NOW!

Download or read book Introduction to the Numerical Solution of Differential Equations written by Douglas Quinney and published by John Wiley & Sons. This book was released on 1987-06-29 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Zhongqiang Zhang
Publisher : Springer
ISBN 13 : 3319575112
Total Pages : 394 pages
Book Rating : 4.17/5 ( download)

DOWNLOAD NOW!

Download or read book Numerical Methods for Stochastic Partial Differential Equations with White Noise written by Zhongqiang Zhang and published by Springer. This book was released on 2017-09-01 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Florian Augustin
Publisher :
ISBN 13 : 9783843903202
Total Pages : 111 pages
Book Rating : 4.04/5 ( download)

DOWNLOAD NOW!

Download or read book Generalized Wiener Expansions for the Numerical Solution of Random Ordinary Differential Equations written by Florian Augustin and published by . This book was released on 2012 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author :
Publisher : Academic Press
ISBN 13 : 9780080955834
Total Pages : 322 pages
Book Rating : 4.35/5 ( download)

DOWNLOAD NOW!

Download or read book Numerical Solution of Ordinary Differential Equations written by and published by Academic Press. This book was released on 1971-03-31 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Author : Gabriel J. Lord
Publisher : Cambridge University Press
ISBN 13 : 1139915770
Total Pages : 516 pages
Book Rating : 4.79/5 ( download)

DOWNLOAD NOW!

Download or read book An Introduction to Computational Stochastic PDEs written by Gabriel J. Lord and published by Cambridge University Press. This book was released on 2014-08-11 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of-the-art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB® codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modelling and materials science.