Download or read book Computer Solution of Ordinary Differential Equations written by Lawrence F. Shampine and published by W.H. Freeman. This book was released on 1975 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Solution of Ordinary Differential Equations written by Kendall Atkinson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.
Download or read book Numerical Methods for Initial Value Problems in Ordinary Differential Equations written by Simeon Ola Fatunla and published by . This book was released on 1988 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analysis for Computer Scientists written by Michael Oberguggenberger and published by Springer Science & Business Media. This book was released on 2011-03-19 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents an algorithmic approach to mathematical analysis, with a focus on modelling and on the applications of analysis. Fully integrating mathematical software into the text as an important component of analysis, the book makes thorough use of examples and explanations using MATLAB, Maple, and Java applets. Mathematical theory is described alongside the basic concepts and methods of numerical analysis, supported by computer experiments and programming exercises, and an extensive use of figure illustrations. Features: thoroughly describes the essential concepts of analysis; provides summaries and exercises in each chapter, as well as computer experiments; discusses important applications and advanced topics; presents tools from vector and matrix algebra in the appendices, together with further information on continuity; includes definitions, propositions and examples throughout the text; supplementary software can be downloaded from the book’s webpage.
Download or read book The Concept of Stability in Numerical Mathematics written by Wolfgang Hackbusch and published by Springer Science & Business Media. This book was released on 2014-02-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the author compares the meaning of stability in different subfields of numerical mathematics. Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of stability holds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methods for ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integral equations. In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.
Download or read book Numerical Solution of Initial Value Problems in Differential Algebraic Equations written by K. E. Brenan and published by SIAM. This book was released on 1996-01-01 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes some of the places where differential-algebraic equations (DAE's) occur.
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Download or read book Numerical Solution of Differential Equations written by Zhilin Li and published by Cambridge University Press. This book was released on 2017-11-30 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.
Download or read book Numerical Solution of Time Dependent Advection Diffusion Reaction Equations written by Willem Hundsdorfer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unique book on Reaction-Advection-Diffusion problems
Download or read book The Numerical Analysis of Ordinary Differential Equations written by J. C. Butcher and published by . This book was released on 1987-02-24 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and computational introduction. The Euler method and its generalizations. Analysis of Runge-Kutta methods. General linear methods.
Download or read book Solving Ordinary Differential Equations II written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Whatever regrets may be, we have done our best." (Sir Ernest Shackleton, turning back on 9 January 1909 at 88°23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential alge braic equations. It contains three chapters: Chapter IV on one-step (Runge Kutta) methods for stiff problems, Chapter Von multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretieal nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered consecutively in each section and indicate, in addition, the section num ber. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.
Download or read book Dynamical Systems and Numerical Analysis written by Andrew Stuart and published by Cambridge University Press. This book was released on 1998-11-28 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.
Download or read book Order Stars written by A. Iserles and published by CRC Press. This book was released on 2020-11-26 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book familiarizes the mathematical community with an analytic tool that is capable of so many applications and presents a list of open problems which might be amenable to analysis with order stars.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Numerical Analysis written by J. Stoer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. We will explain some of these techniques in connection with the Cholesky algorithm for solving positive definite linear systems. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm; the sections on the LR and QR algorithm were rewritten and now contain a description of implicit shift techniques. In order to some extent take into account the progress in the area of ordinary differential equations, a new section on implicit differential equa tions and differential-algebraic systems was added, and the section on stiff differential equations was updated by describing further methods to solve such equations.
Download or read book Numerical Solution of Ordinary Differential Equations written by Kendall Atkinson and published by John Wiley & Sons. This book was released on 2009-02-09 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introduction to numerical methodsand the mathematical framework neededto understand their performance Numerical Solution of Ordinary Differential Equations presents a complete and easy-to-follow introduction to classical topics in the numerical solution of ordinary differential equations. The book's approach not only explains the presented mathematics, but also helps readers understand how these numerical methods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringing together and categorizing different types of problems in order to help readers comprehend the applications of ordinary differential equations. In addition, the authors' collective academic experience ensures a coherent and accessible discussion of key topics, including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to test and build their knowledge of the presented methods, and a related Web site features MATLAB® programs that facilitate the exploration of numerical methods in greater depth. Detailed references outline additional literature on both analytical and numerical aspects of ordinary differential equations for further exploration of individual topics. Numerical Solution of Ordinary Differential Equations is an excellent textbook for courses on the numerical solution of differential equations at the upper-undergraduate and beginning graduate levels. It also serves as a valuable reference for researchers in the fields of mathematics and engineering.
Download or read book Modeling of Atmospheric Chemistry written by Guy P. Brasseur and published by Cambridge University Press. This book was released on 2017-06-19 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modeling of atmospheric composition is a formidable scientific and computational challenge. This comprehensive presentation of the modeling methods used in atmospheric chemistry focuses on both theory and practice, from the fundamental principles behind models, through to their applications in interpreting observations. An encyclopaedic coverage of methods used in atmospheric modeling, including their advantages and disadvantages, makes this a one-stop resource with a large scope. Particular emphasis is given to the mathematical formulation of chemical, radiative, and aerosol processes; advection and turbulent transport; emission and deposition processes; as well as major chapters on model evaluation and inverse modeling. The modeling of atmospheric chemistry is an intrinsically interdisciplinary endeavour, bringing together meteorology, radiative transfer, physical chemistry and biogeochemistry, making the book of value to a broad readership. Introductory chapters and a review of the relevant mathematics make this book instantly accessible to graduate students and researchers in the atmospheric sciences.
