Random Differential Equations in Scientific Computing

Random Differential Equations in Scientific Computing

Author: Tobias Neckel

Publisher: Walter de Gruyter

Published: 2013-12-17

Total Pages: 650

ISBN-13: 8376560263

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This book is a holistic and self-contained treatment of the analysis and numerics of random differential equations from a problem-centred point of view. An interdisciplinary approach is applied by considering state-of-the-art concepts of both dynamical systems and scientific computing. The red line pervading this book is the two-fold reduction of a random partial differential equation disturbed by some external force as present in many important applications in science and engineering. First, the random partial differential equation is reduced to a set of random ordinary differential equations in the spirit of the method of lines. These are then further reduced to a family of (deterministic) ordinary differential equations. The monograph will be of benefit, not only to mathematicians, but can also be used for interdisciplinary courses in informatics and engineering.


Random Differential Equations in Scientific Computing

Random Differential Equations in Scientific Computing

Author: Tobias Neckel

Publisher:

Published: 2013

Total Pages: 624

ISBN-13: 9788376560243

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"This book is a holistic and self-contained treatment of the analysis and numerics of random differential equations from a problem-centered point of view. We take an interdisciplinary approach by considering state-of-the-art concepts of both dynamical systems and scientific computing. [...] The areas covered here are of importance for interdisciplinary courses in informatics, engineering and mathematics. [...] From a methodological point of view, the red line pervading this book is the two-fold reduction of a random partial differential equation disturbed by some external force as present in many important applications in science and engineering." --Preface, pages iii-iv.


Scientific Computing

Scientific Computing

Author: Michael T. Heath

Publisher: SIAM

Published: 2018-11-14

Total Pages: 587

ISBN-13: 1611975573

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This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results.? In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.


Random Ordinary Differential Equations and Their Numerical Solution

Random Ordinary Differential Equations and Their Numerical Solution

Author: Xiaoying Han

Publisher: Springer

Published: 2017-10-25

Total Pages: 252

ISBN-13: 981106265X

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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.


Scientific Computing with Case Studies

Scientific Computing with Case Studies

Author: Dianne P. O'Leary

Publisher: SIAM

Published: 2009-03-19

Total Pages: 376

ISBN-13: 0898716667

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This book is a practical guide to the numerical solution of linear and nonlinear equations, differential equations, optimization problems, and eigenvalue problems. It treats standard problems and introduces important variants such as sparse systems, differential-algebraic equations, constrained optimization, Monte Carlo simulations, and parametric studies. Stability and error analysis are emphasized, and the Matlab algorithms are grounded in sound principles of software design and understanding of machine arithmetic and memory management. Nineteen case studies provide experience in mathematical modeling and algorithm design, motivated by problems in physics, engineering, epidemiology, chemistry, and biology. The topics included go well beyond the standard first-course syllabus, introducing important problems such as differential-algebraic equations and conic optimization problems, and important solution techniques such as continuation methods. The case studies cover a wide variety of fascinating applications, from modeling the spread of an epidemic to determining truss configurations.


Computational Mathematics and Applications

Computational Mathematics and Applications

Author: Dia Zeidan

Publisher: Springer Nature

Published: 2020-11-23

Total Pages: 277

ISBN-13: 9811584982

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This book is a collection of invited and reviewed chapters on state-of-the-art developments in interdisciplinary mathematics. The book discusses recent developments in the fields of theoretical and applied mathematics, covering areas of interest to mathematicians, scientists, engineers, industrialists, researchers, faculty, and students. Readers will be exposed to topics chosen from a wide range of areas including differential equations, integral reforms, operational calculus, numerical analysis, fluid mechanics, and computer science. The aim of the book is to provide brief and reliably expressed research topics that will enable those new or not aware of mathematical sciences in this part of the world. While the book has not been precisely planned to address any branch of mathematics, it presents contributions of the relevant topics to do so. The topics chosen for the book are those that we have found of significant interest to many researchers in the world. These also are topics that are applicable in many fields of computational and applied mathematics. This book constitutes the first attempt in Jordanian literature to scientifically consider the extensive need of research development at the national and international levels with which mathematics deals. The book grew not only from the international collaboration between the authors but rather from the long need for a research-based book from different parts of the world for researchers and professionals working in computational and applied mathematics. This is the modified version of the back-cover content on the print book


Computational Differential Equations

Computational Differential Equations

Author: Kenneth Eriksson

Publisher: Cambridge University Press

Published: 1996-09-05

Total Pages: 558

ISBN-13: 9780521567381

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This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.


Recent Advances in Scientific Computing and Applications

Recent Advances in Scientific Computing and Applications

Author: Jichun Li

Publisher: American Mathematical Soc.

Published: 2013-04-24

Total Pages: 397

ISBN-13: 0821887378

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This volume contains the proceedings of the Eighth International Conference on Scientific Computing and Applications, held April 1-4, 2012, at the University of Nevada, Las Vegas. The papers in this volume cover topics such as finite element methods, multiscale methods, finite difference methods, spectral methods, collocation methods, adaptive methods, parallel computing, linear solvers, applications to fluid flow, nano-optics, biofilms, finance, magnetohydrodynamics flow, electromagnetic waves, the fluid-structure interaction problem, and stochastic PDEs. This book will serve as an excellent reference for graduate students and researchers interested in scientific computing and its applications.


Applied Stochastic Differential Equations

Applied Stochastic Differential Equations

Author: Simo Särkkä

Publisher: Cambridge University Press

Published: 2019-05-02

Total Pages: 327

ISBN-13: 1316510085

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With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.