Differential Equations And Numerical Mathematics
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| Author | : Stig Larsson |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 263 |
| Release | : 2008-12-05 |
| Genre | : Mathematics |
| ISBN | : 3540887059 |
Download Partial Differential Equations with Numerical Methods Book in PDF, Epub and Kindle
The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.
| Author | : J.R. Dormand |
| Publisher | : CRC Press |
| Total Pages | : 385 |
| Release | : 2018-05-04 |
| Genre | : Mathematics |
| ISBN | : 1351083554 |
Download Numerical Methods for Differential Equations Book in PDF, Epub and Kindle
With emphasis on modern techniques, Numerical Methods for Differential Equations: A Computational Approach covers the development and application of methods for the numerical solution of ordinary differential equations. Some of the methods are extended to cover partial differential equations. All techniques covered in the text are on a program disk included with the book, and are written in Fortran 90. These programs are ideal for students, researchers, and practitioners because they allow for straightforward application of the numerical methods described in the text. The code is easily modified to solve new systems of equations. Numerical Methods for Differential Equations: A Computational Approach also contains a reliable and inexpensive global error code for those interested in global error estimation. This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use. It is also an excellent reference and source of software for researchers and practitioners who need computer solutions to differential equations.
| Author | : Mark H. Holmes |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 248 |
| Release | : 2007-04-05 |
| Genre | : Mathematics |
| ISBN | : 0387681213 |
Download Introduction to Numerical Methods in Differential Equations Book in PDF, Epub and Kindle
This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises, which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.
| Author | : J. C. Butcher |
| Publisher | : John Wiley & Sons |
| Total Pages | : 442 |
| Release | : 2004-08-20 |
| Genre | : Mathematics |
| ISBN | : 0470868260 |
Download Numerical Methods for Ordinary Differential Equations Book in PDF, Epub and Kindle
This new book updates the exceptionally popular Numerical Analysis of Ordinary Differential Equations. "This book is...an indispensible reference for any researcher."-American Mathematical Society on the First Edition. Features: * New exercises included in each chapter. * Author is widely regarded as the world expert on Runge-Kutta methods * Didactic aspects of the book have been enhanced by interspersing the text with exercises. * Updated Bibliography.
| Author | : David F. Griffiths |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 274 |
| Release | : 2010-11-11 |
| Genre | : Mathematics |
| ISBN | : 0857291483 |
Download Numerical Methods for Ordinary Differential Equations Book in PDF, Epub and Kindle
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 highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors. The book covers key foundation topics: o Taylor series methods o Runge--Kutta methods o Linear multistep methods o Convergence o Stability and a range of modern themes: o Adaptive stepsize selection o Long term dynamics o Modified equations o Geometric integration o Stochastic differential equations The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com
| Author | : Uri M. Ascher |
| Publisher | : SIAM |
| Total Pages | : 620 |
| Release | : 1994-12-01 |
| Genre | : Mathematics |
| ISBN | : 9781611971231 |
Download Numerical Solution of Boundary Value Problems for Ordinary Differential Equations Book in PDF, Epub and Kindle
This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
| Author | : G. Evans |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 308 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1447103793 |
Download Analytic Methods for Partial Differential Equations Book in PDF, Epub and Kindle
This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.
| Author | : Hans-Görg Roos |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 599 |
| Release | : 2008-09-17 |
| Genre | : Mathematics |
| ISBN | : 3540344675 |
Download Robust Numerical Methods for Singularly Perturbed Differential Equations Book in PDF, Epub and Kindle
This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.
| Author | : Peter Knabner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 437 |
| Release | : 2003-06-26 |
| Genre | : Mathematics |
| ISBN | : 038795449X |
Download Numerical Methods for Elliptic and Parabolic Partial Differential Equations Book in PDF, Epub and Kindle
This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.
| Author | : Joël Chaskalovic |
| Publisher | : Springer |
| Total Pages | : 362 |
| Release | : 2014-05-16 |
| Genre | : Mathematics |
| ISBN | : 3319035630 |
Download Mathematical and Numerical Methods for Partial Differential Equations Book in PDF, Epub and Kindle
This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic.
