Random Differential Equations In Scientific Computing

Download or read book Random Differential Equations in Scientific Computing written by Tobias Neckel and published by Walter de Gruyter. This book was released on 2013-12-17 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Random Differential Equations in Science and Engineering written by Soong and published by Academic Press. This book was released on 1973-09-21 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random Differential Equations in Science and Engineering

Download or read book Random Differential Equations in Scientific Computing written by Tobias Neckel and published by . This book was released on 2013 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

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 252 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.

Download or read book Scientific Computing written by Michael T. Heath and published by SIAM. This book was released on 2018-11-14 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Scientific Computing with Case Studies written by Dianne P. O'Leary and published by SIAM. This book was released on 2009-03-19 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Computational Differential Equations written by Kenneth Eriksson and published by Cambridge University Press. This book was released on 1996-09-05 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.