A First Course In The Numerical Analysis Of Differential Equations
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A First Course In The Numerical Analysis Of Differential Equations
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Author : A. Iserles
language : en
Publisher: Cambridge University Press
Release Date : 2009
A First Course In The Numerical Analysis Of Differential Equations written by A. Iserles and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.
A First Course In The Numerical Analysis Of Differential Equations
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Author : Arieh Iserles
language : en
Publisher: Cambridge University Press
Release Date : 2008-11-27
A First Course In The Numerical Analysis Of Differential Equations written by Arieh Iserles and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-27 with Mathematics categories.
Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This second edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.
A First Course In Numerical Analysis
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Author : Anthony Ralston
language : en
Publisher: Courier Corporation
Release Date : 2001-01-01
A First Course In Numerical Analysis written by Anthony Ralston and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
Outstanding text, oriented toward computer solutions, stresses errors in methods and computational efficiency. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.
A First Course In Ordinary Differential Equations
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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.
A First Course In The Numerical Analysis Of Differential Equations
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Author : Arieh Iserles
language : en
Publisher:
Release Date : 2009
A First Course In The Numerical Analysis Of Differential Equations written by Arieh Iserles and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Numerical Methods For Ordinary Differential Equations
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Author : David F. Griffiths
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-11
Numerical Methods For Ordinary Differential Equations written by David F. Griffiths 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 2010-11-11 with Mathematics categories.
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
Numerical Partial Differential Equations For Environmental Scientists And Engineers
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Author : Daniel R. Lynch
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-12-15
Numerical Partial Differential Equations For Environmental Scientists And Engineers written by Daniel R. Lynch 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 2004-12-15 with Science categories.
For readers with some competence in PDE solution properties, this book offers an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It presents two major discretization methods: Finite Difference and Finite Element, plus a section on practical approaches to ill-posed problems. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems.
Introduction To Numerical Methods In Differential Equations
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Author : Mark H. Holmes
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-05
Introduction To Numerical Methods In Differential Equations written by Mark H. Holmes 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 2007-04-05 with Mathematics categories.
The title gives a reasonable ?rst-order approximation to what this book is about. To explain why, let’s start with the expression “di?erential equations.” These are essential in science and engineering, because the laws of nature t- ically result in equations relating spatial and temporal changes in one or more variables.Todevelopanunderstandingofwhatisinvolvedin?ndingsolutions, the book begins with problems involving derivatives for only one independent variable, and these give rise to ordinary di?erential equations. Speci?cally, the ?rst chapter considers initial value problems (time derivatives), and the second concentrates on boundary value problems (space derivatives). In the succeeding four chapters problems involving both time and space derivatives, partial di?erential equations, are investigated. This brings us to the next expression in the title: “numerical methods.” This is a book about how to transform differential equations into problems that can be solved using a computer.The fact is that computers are only able to solve discrete problems and generally do this using ?nite-precision arithmetic. What this means is that in deriving and then using a numerical algorithmthecorrectnessofthediscreteapproximationmustbeconsidered,as must the consequences of round-o? error in using ?oating-point arithmetic to calculatetheanswer.Oneoftheinterestingaspectsofthesubjectisthatwhat appears to be an obviously correct numerical method can result in complete failure. Consequently, although the book concentrates on the derivation and use of numerical methods, the theoretical underpinnings are also presented andusedinthedevelopment.
A First Course In Differential Equations
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Author : J. David Logan
language : en
Publisher: Springer Science & Business Media
Release Date : 2006
A First Course In Differential Equations written by J. David Logan 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 2006 with Mathematics categories.
This book is intended as an alternative to the standard differential equations text, which typically includes a large collection of methods and applications, packaged with state-of-the-art color graphics, student solution manuals, the latest fonts, marginal notes, and web-based supplements. These texts adds up to several hundred pages of text and can be very expensive for students to buy. Many students do not have the time or desire to read voluminous texts and explore internet supplements. Here, however, the author writes concisely, to the point, and in plain language. Many examples and exercises are included. In addition, this text also encourages students to use a computer algebra system to solve problems numerically, and as such, templates of MATLAB programs that solve differential equations are given in an appendix, as well as basic Maple and Mathematica commands.