Numerical Methods For Initial Value Problems In Physics
DOWNLOAD
Download Numerical Methods For Initial Value Problems In Physics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Numerical Methods For Initial Value Problems In Physics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Numerical Methods For Initial Value Problems In Physics
DOWNLOAD
Author : Francisco S. Guzmán
language : en
Publisher: Springer Nature
Release Date : 2023-08-23
Numerical Methods For Initial Value Problems In Physics written by Francisco S. Guzmán and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-23 with Science categories.
This textbook is a comprehensive overview of the construction, implementation, and application of important numerical methods for the solution of Initial Value Problems (IVPs). Beginning with IVPs involving Ordinary Differential Equations (ODEs) and progressing to problems with Partial Differential Equations (PDEs) in 1+1 and 3+1 dimensions, it provides readers with a clear and systematic progression from simple to complex concepts. The numerical methods selected in this textbook can solve a considerable variety of problems and the applications presented cover a wide range of topics, including population dynamics, chaos, celestial mechanics, geophysics, astrophysics, and more. Each chapter contains a variety of solved problems and exercises, with code included. These examples are designed to motivate and inspire readers to delve deeper into the state-of-the-art problems in their own fields. The code is written in Fortran 90, in a library-free style, making them easy to program and efficient to run. The appendix also includes the same code in C++, making the book accessible to a variety of programming backgrounds. At the end of each chapter, there are brief descriptions of how the methods could be improved, along with one or two projects that can be developed with the methods and codes described. These projects are highly engaging, from synchronization of chaos and message encryption to gravitational waves emitted by a binary system and non-linear absorption of a scalar field. With its clear explanations, hands-on approach, and practical examples, this textbook is an essential resource for advanced undergraduate and graduate students who want to the learn how to use numerical methods to tackle challenging problems.
Difference Methods For Initial Boundary Value Problems And Flow Around Bodies
DOWNLOAD
Author : You-lan Zhu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Difference Methods For Initial Boundary Value Problems And Flow Around Bodies written by You-lan Zhu 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 2013-06-29 with Mathematics categories.
Since the appearance of computers, numerical methods for discontinuous solutions of quasi-linear hyperbolic systems of partial differential equations have been among the most important research subjects in numerical analysis. The authors have developed a new difference method (named the singularity-separating method) for quasi-linear hyperbolic systems of partial differential equations. Its most important feature is that it possesses a high accuracy even for problems with singularities such as schocks, contact discontinuities, rarefaction waves and detonations. Besides the thorough description of the method itself, its mathematical foundation (stability-convergence theory of difference schemes for initial-boundary-value hyperbolic problems) and its application to supersonic flow around bodies are discussed. Further, the method of lines and its application to blunt body problems and conical flow problems are described in detail. This book should soon be an important working basis for both graduate students and researchers in the field of partial differential equations as well as in mathematical physics.
Discrete Numerical Methods In Physics And Engineering
DOWNLOAD
Author : Greenspan
language : en
Publisher: Academic Press
Release Date : 1974-05-31
Discrete Numerical Methods In Physics And Engineering written by Greenspan and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-05-31 with Computers categories.
Discrete Numerical Methods in Physics and Engineering
Difference Methods For Initial Value Problems
DOWNLOAD
Author : Robert D. Richtmyer
language : en
Publisher:
Release Date : 2013-09
Difference Methods For Initial Value Problems written by Robert D. Richtmyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09 with categories.
Difference Methods For Initial Value Problems
DOWNLOAD
Author : Robert D. Richtmyer
language : en
Publisher:
Release Date : 1967-01-15
Difference Methods For Initial Value Problems written by Robert D. Richtmyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967-01-15 with Mathematics categories.
Numerical Methods For Ordinary Differential Equations
DOWNLOAD
Author : J. C. Butcher
language : en
Publisher: John Wiley & Sons
Release Date : 2016-08-29
Numerical Methods For Ordinary Differential Equations written by J. C. Butcher and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-29 with Mathematics categories.
A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world’s leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a cornerstone of modern applied mathematics. In addition to serving as a broad and comprehensive study of numerical methods for initial value problems, this book contains a special emphasis on Runge-Kutta methods by the mathematician who transformed the subject into its modern form dating from his classic 1963 and 1972 papers. A second feature is general linear methods which have now matured and grown from being a framework for a unified theory of a wide range of diverse numerical schemes to a source of new and practical algorithms in their own right. As the founder of general linear method research, John Butcher has been a leading contributor to its development; his special role is reflected in the text. The book is written in the lucid style characteristic of the author, and combines enlightening explanations with rigorous and precise analysis. In addition to these anticipated features, the book breaks new ground by including the latest results on the highly efficient G-symplectic methods which compete strongly with the well-known symplectic Runge-Kutta methods for long-term integration of conservative mechanical systems. This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for research workers in applied mathematics, physics and engineering.
Numerical Solution Of Ordinary Differential Equations
DOWNLOAD
Author : Donald Greenspan
language : en
Publisher: John Wiley & Sons
Release Date : 2008-09-26
Numerical Solution Of Ordinary Differential Equations written by Donald Greenspan and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-26 with Science categories.
This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic systems. The examples are carefully explained and compiled into an algorithm, each of which is presented independent of a specific programming language. Each chapter is rounded off with exercises.
Difference Methods For Initial Value Problems
DOWNLOAD
Author : Robert D. Richtmyer
language : en
Publisher:
Release Date : 1957
Difference Methods For Initial Value Problems written by Robert D. Richtmyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with Mathematics categories.
A First Course In Ordinary Differential Equations
DOWNLOAD
Author : Martin Hermann
language : en
Publisher: Springer Science & Business
Release Date : 2014-04-22
A First Course In Ordinary Differential Equations written by Martin Hermann and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-22 with Mathematics categories.
This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed that the reader has a basic grasp of elementary calculus, in particular methods of integration, and of numerical analysis. Physicists, chemists, biologists, computer scientists and engineers whose work involves solving ODEs will also find the book useful as a reference work and tool for independent study. The book has been prepared within the framework of a German–Iranian research project on mathematical methods for ODEs, which was started in early 2012.
Numerical Time Dependent Partial Differential Equations For Scientists And Engineers
DOWNLOAD
Author : Moysey Brio
language : en
Publisher: Academic Press
Release Date : 2010-09-21
Numerical Time Dependent Partial Differential Equations For Scientists And Engineers written by Moysey Brio and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-21 with Mathematics categories.
It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations