Вычислительная математика
Математика
  • формат djvu
  • размер 1.75 МБ
  • добавлен 10 декабря 2010 г.
Ascher U.M., Petzold L.R. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Society for Industrial and Applied Mathematics, 1998. - 332 pages.

Designed for those people who want to gain a practical knowledge of mode techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. Written by two of the field's leading authorities, it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential-algebraic equations. The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. This is a practical and mathematically well informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included.
Похожие разделы
Смотрите также

Burden R.L., Faires J.D. Numerical Analysis

  • формат djvu
  • размер 7.32 МБ
  • добавлен 22 ноября 2009 г.
Cengage Learning, 2001, 850 pp. , 7 edition. Mathematical preliminaries. solutions of equations in one variable. interpolation and polynomial approximation. numerical differentiation and integration. initial-Value problems for ordinary differential equations. direct methods for solving linear systems. iterative techniques in matrix algebra. approximation theory. approximating eigenvalues. numerical solutions of nonlinear systems of equations. bou...

Butcher J.C. Numerical Methods for Ordinary Differential Equations

  • формат djvu
  • размер 3.12 МБ
  • добавлен 27 декабря 2011 г.
John Wiley & Sons Ltd, 2003. – 440 pages. This book represents an attempt to modernize and expand the previous volume 'The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods'. It is more modern in that it considers several topics that had not yet emerged as important research areas when the former book was written. It is expanded in that it contains a comprehensive treatment of linear multistep metho...

Gavrilyuk I.P., Makarov V.L., Vasylyk V. Exponentially Convergent Algorithms for Abstract Differential Equations

  • формат pdf
  • размер 2.02 МБ
  • добавлен 18 октября 2011 г.
Springer, 2011. - 538 pages. This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as of partial differential equations (PDEs) descri...

Geiser J. Iterative Splitting Methods for Differential Equations

  • формат pdf
  • размер 9.34 МБ
  • добавлен 16 августа 2011 г.
CRC, 2011. - 320 pages. Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems...

Golub G.H., Ortega J.M. Scientific Computing and Differential Equations: An Introduction to Numerical Methods

  • формат djvu
  • размер 3.5 МБ
  • добавлен 12 декабря 2010 г.
Academic Press, 1991. - 344 pages. Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places...

Griffiths D.F., Higham D.J. Numerical Methods for Ordinary Differential Equations: Initial Value Problems

  • формат pdf
  • размер 7.84 МБ
  • добавлен 10 декабря 2010 г.
Springer, 2010. - 268 pages. 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 highlig...

Hairer E., Wanner G. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems

  • формат pdf
  • размер 57.95 МБ
  • добавлен 14 декабря 2010 г.
Springer, 2010. - 614 pages. The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). The book is divided into four chapters. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergenc...

Iserles A. A First Course in the Numerical Analysis of Differential Equations

  • формат djvu
  • размер 3.96 МБ
  • добавлен 10 декабря 2010 г.
Cambridge University Press, 1996. - 400 Pages This book presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance among theoretical, algorithmic and applied aspects of the subject. In detail, topics covered include numerical solution of ordinary differential equations by multistep and Runge-Kutt...

Kloeden P.E., Platen E. Numerical Solution of Stochastic Differential Equations

  • формат djvu
  • размер 5.59 МБ
  • добавлен 30 декабря 2010 г.
Springer, 1995. - 636 pages. The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations, due to the peculiarities of stochastic calculus. The book proposes to the reader whose background knowledge is limited to undergraduate level methods for engineering and physics, and easily accessible introductions to SDE and then applications as well as the numerical methods for dealing wit...

Schlesser W.E., Griffiths G.W. A Compendium of Partial Differential Equation Models: Method of Lines Analysis with Matlab

  • формат pdf
  • размер 6.41 МБ
  • добавлен 23 января 2011 г.
Cambridge University, 2009. - 490 Pages. A Compendium of Partial Differential Equation Models presents numerical methods and associated computer codes in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs), one of the mostly widely used forms of mathematics in science and engineering. The authors focus on the method of lines (MOL), a well-established numerical procedure for all major classes of PDEs...