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A First Course in the Numerical Analysis of Differential Equations

Author: Arieh Iserles

Publisher: Cambridge University Press

Published: 2008-11-27

Total Pages: 481

ISBN-13: 113947376X

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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.

Book Synopsis A First Course in the Numerical Analysis of Differential Equations by : Arieh Iserles

Download or read book A First Course in the Numerical Analysis of Differential Equations written by Arieh Iserles and published by Cambridge University Press. This book was released on 2008-11-27 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 the Numerical Analysis of Differential Equations

Author: A. Iserles

Publisher: Cambridge University Press

Published: 2009

Total Pages: 481

ISBN-13: 0521734908

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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.

Book Synopsis A First Course in the Numerical Analysis of Differential Equations by : A. Iserles

Download or read book A First Course in the Numerical Analysis of Differential Equations written by A. Iserles and published by Cambridge University Press. This book was released on 2009 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Ordinary Differential Equations

Author: Martin Hermann

Publisher: Springer Science & Business

Published: 2014-04-22

Total Pages: 300

ISBN-13: 8132218353

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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.

Book Synopsis A First Course in Ordinary Differential Equations by : Martin Hermann

Download or read book A First Course in Ordinary Differential Equations written by Martin Hermann and published by Springer Science & Business. This book was released on 2014-04-22 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Numerical Analysis

Author: Anthony Ralston

Publisher: Courier Corporation

Published: 2001-01-01

Total Pages: 644

ISBN-13: 9780486414546

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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.

Book Synopsis A First Course in Numerical Analysis by : Anthony Ralston

Download or read book A First Course in Numerical Analysis written by Anthony Ralston and published by Courier Corporation. This book was released on 2001-01-01 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Numerical Methods

Author: Uri M. Ascher

Publisher: SIAM

Published: 2011-07-14

Total Pages: 574

ISBN-13: 0898719976

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Offers students a practical knowledge of modern techniques in scientific computing.

Book Synopsis A First Course in Numerical Methods by : Uri M. Ascher

Download or read book A First Course in Numerical Methods written by Uri M. Ascher and published by SIAM. This book was released on 2011-07-14 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers students a practical knowledge of modern techniques in scientific computing.

A First Course in Differential Equations

Author: J. David Logan

Publisher: Springer Science & Business Media

Published: 2006-05-20

Total Pages: 297

ISBN-13: 0387299300

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Therearemanyexcellenttextsonelementarydi?erentialequationsdesignedfor the standard sophomore course. However, in spite of the fact that most courses are one semester in length, the texts have evolved into calculus-like pres- tations that include a large collection of methods and applications, packaged with student manuals, and Web-based notes, projects, and supplements. All of this comes in several hundred pages of text with busy formats. Most students do not have the time or desire to read voluminous texts and explore internet supplements. The format of this di?erential equations book is di?erent; it is a one-semester, brief treatment of the basic ideas, models, and solution methods. Itslimitedcoverageplacesitsomewherebetweenanoutlineandadetailedte- book. I have tried to write concisely, to the point, and in plain language. Many worked examples and exercises are included. A student who works through this primer will have the tools to go to the next level in applying di?erential eq- tions to problems in engineering, science, and applied mathematics. It can give some instructors, who want more concise coverage, an alternative to existing texts.

Book Synopsis A First Course in Differential Equations by : J. David Logan

Download or read book A First Course in Differential Equations written by J. David Logan and published by Springer Science & Business Media. This book was released on 2006-05-20 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Therearemanyexcellenttextsonelementarydi?erentialequationsdesignedfor the standard sophomore course. However, in spite of the fact that most courses are one semester in length, the texts have evolved into calculus-like pres- tations that include a large collection of methods and applications, packaged with student manuals, and Web-based notes, projects, and supplements. All of this comes in several hundred pages of text with busy formats. Most students do not have the time or desire to read voluminous texts and explore internet supplements. The format of this di?erential equations book is di?erent; it is a one-semester, brief treatment of the basic ideas, models, and solution methods. Itslimitedcoverageplacesitsomewherebetweenanoutlineandadetailedte- book. I have tried to write concisely, to the point, and in plain language. Many worked examples and exercises are included. A student who works through this primer will have the tools to go to the next level in applying di?erential eq- tions to problems in engineering, science, and applied mathematics. It can give some instructors, who want more concise coverage, an alternative to existing texts.

Numerical Analysis of Partial Differential Equations

Author: S. H, Lui

Publisher: John Wiley & Sons

Published: 2012-01-10

Total Pages: 506

ISBN-13: 1118111117

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A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.

Book Synopsis Numerical Analysis of Partial Differential Equations by : S. H, Lui

Download or read book Numerical Analysis of Partial Differential Equations written by S. H, Lui and published by John Wiley & Sons. This book was released on 2012-01-10 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.

Numerical Methods for Ordinary Differential Equations

Author: David F. Griffiths

Publisher: Springer Science & Business Media

Published: 2010-11-11

Total Pages: 274

ISBN-13: 0857291483

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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

Book Synopsis Numerical Methods for Ordinary Differential Equations by : David F. Griffiths

Download or read book Numerical Methods for Ordinary Differential Equations written by David F. Griffiths and published by Springer Science & Business Media. This book was released on 2010-11-11 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Advanced Numerical Methods for Differential Equations

Author: Harendra Singh

Publisher: CRC Press

Published: 2021-07-29

Total Pages: 336

ISBN-13: 1000381080

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Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.

Book Synopsis Advanced Numerical Methods for Differential Equations by : Harendra Singh

Download or read book Advanced Numerical Methods for Differential Equations written by Harendra Singh and published by CRC Press. This book was released on 2021-07-29 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.

Numerical Partial Differential Equations for Environmental Scientists and Engineers

Author: Daniel R. Lynch

Publisher: Springer Science & Business Media

Published: 2006-06-02

Total Pages: 390

ISBN-13: 0387236201

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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.

Book Synopsis Numerical Partial Differential Equations for Environmental Scientists and Engineers by : Daniel R. Lynch

Download or read book Numerical Partial Differential Equations for Environmental Scientists and Engineers written by Daniel R. Lynch and published by Springer Science & Business Media. This book was released on 2006-06-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.