Numerical Analysis Of Systems Of Ordinary And Stochastic Differential Equations
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Numerical Analysis Of Systems Of Ordinary And Stochastic Differential Equations
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Author : S. S. Artemiev
language : en
Publisher: Walter de Gruyter
Release Date : 2011-02-11
Numerical Analysis Of Systems Of Ordinary And Stochastic Differential Equations written by S. S. Artemiev and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-11 with Mathematics categories.
No detailed description available for "Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations".
Numerical Solution Of Stochastic Differential Equations
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Author : Peter E. Kloeden
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Numerical Solution Of Stochastic Differential Equations written by Peter E. Kloeden 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 2013-04-17 with Mathematics categories.
The aim of this book is to provide an accessible introduction to stochastic differ ential equations and their applications together with a systematic presentation of methods available for their numerical solution. During the past decade there has been an accelerating interest in the de velopment of numerical methods for stochastic differential equations (SDEs). This activity has been as strong in the engineering and physical sciences as it has in mathematics, resulting inevitably in some duplication of effort due to an unfamiliarity with the developments in other disciplines. Much of the reported work has been motivated by the need to solve particular types of problems, for which, even more so than in the deterministic context, specific methods are required. The treatment has often been heuristic and ad hoc in character. Nevertheless, there are underlying principles present in many of the papers, an understanding of which will enable one to develop or apply appropriate numerical schemes for particular problems or classes of problems.
Numerical Methods For Ordinary Differential Equations
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Author : David F. Griffiths
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-11
Numerical Methods For Ordinary Differential Equations written by David F. Griffiths 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 2010-11-11 with Mathematics categories.
Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors. The book covers key foundation topics: o Taylor series methods o Runge--Kutta methods o Linear multistep methods o Convergence o Stability and a range of modern themes: o Adaptive stepsize selection o Long term dynamics o Modified equations o Geometric integration o Stochastic differential equations The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com
Applied Stochastic Differential Equations
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Author : Simo Särkkä
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-02
Applied Stochastic Differential Equations written by Simo Särkkä and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-02 with Business & Economics categories.
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Stochastic Differential Equations On Manifolds
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Author : K. D. Elworthy
language : en
Publisher: Cambridge University Press
Release Date : 1982
Stochastic Differential Equations On Manifolds written by K. D. Elworthy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Manifolds (Mathematics). categories.
The aims of this book, originally published in 1982, are to give an understanding of the basic ideas concerning stochastic differential equations on manifolds and their solution flows, to examine the properties of Brownian motion on Riemannian manifolds when it is constructed using the stochiastic development and to indicate some of the uses of the theory. The author has included two appendices which summarise the manifold theory and differential geometry needed to follow the development; coordinate-free notation is used throughout. Moreover, the stochiastic integrals used are those which can be obtained from limits of the Riemann sums, thereby avoiding much of the technicalities of the general theory of processes and allowing the reader to get a quick grasp of the fundamental ideas of stochastic integration as they are needed for a variety of applications.
Random Ordinary Differential Equations And Their Numerical Solution
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Author : Xiaoying Han
language : en
Publisher: Springer
Release Date : 2017-10-25
Random Ordinary Differential Equations And Their Numerical Solution written by Xiaoying Han and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-25 with Mathematics categories.
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.
Numerical Solution Of Ordinary Differential Equations
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Author : L.F. Shampine
language : en
Publisher: CRC Press
Release Date : 1994-03-01
Numerical Solution Of Ordinary Differential Equations written by L.F. Shampine and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-03-01 with Mathematics categories.
This book is an introduction to the numerical solution of the initial value problem for a system of ordinary differential equations (ODEs). It describes how typical problems can be formulated in a way that permits their solution with standard codes.
The Numerical Solution Of Ordinary And Partial Differential Equations
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Author : Granville Sewell
language : en
Publisher: Academic Press
Release Date : 2014-05-10
The Numerical Solution Of Ordinary And Partial Differential Equations written by Granville Sewell and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
The Numerical Solution of Ordinary and Partial Differential Equations is an introduction to the numerical solution of ordinary and partial differential equations. Finite difference methods for solving partial differential equations are mostly classical low order formulas, easy to program but not ideal for problems with poorly behaved solutions or (especially) for problems in irregular multidimensional regions. FORTRAN77 programs are used to implement many of the methods studied. Comprised of six chapters, this book begins with a review of direct methods for the solution of linear systems, with emphasis on the special features of the linear systems that arise when differential equations are solved. The next four chapters deal with the more commonly used finite difference methods for solving a variety of problems, including both ordinary differential equations and partial differential equations, and both initial value and boundary value problems. The final chapter is an overview of the basic ideas behind the finite element method and covers the Galerkin method for boundary value problems. Examples using piecewise linear trial functions, cubic hermite trial functions, and triangular elements are presented. This monograph is appropriate for senior-level undergraduate or first-year graduate students of mathematics.
From Elementary Probability To Stochastic Differential Equations With Maple
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Author : Sasha Cyganowski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
From Elementary Probability To Stochastic Differential Equations With Maple written by Sasha Cyganowski 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 2012-12-06 with Mathematics categories.
This is an introduction to probabilistic and statistical concepts necessary to understand the basic ideas and methods of stochastic differential equations. Based on measure theory, which is introduced as smoothly as possible, it provides practical skills in the use of MAPLE in the context of probability and its applications. It offers to graduates and advanced undergraduates an overview and intuitive background for more advanced studies.
An Introduction To The Numerical Simulation Of Stochastic Differential Equations
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Author : Desmond J. Higham
language : en
Publisher:
Release Date : 2020-12
An Introduction To The Numerical Simulation Of Stochastic Differential Equations written by Desmond J. Higham and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12 with categories.