Finite Difference Computing with PDEs
Finite Difference Computing with PDEs

Author: Hans Petter Langtangen

Publisher: Springer

Published: 2017-06-21

Total Pages: 522

ISBN-13: 3319554565

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This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Finite Difference Methods for Ordinary and Partial Differential Equations
Finite Difference Methods for Ordinary and Partial Differential Equations

Author: Randall J. LeVeque

Publisher: SIAM

Published: 2007-01-01

Total Pages: 356

ISBN-13: 9780898717839

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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.

Numerical Partial Differential Equations: Finite Difference Methods
Numerical Partial Differential Equations: Finite Difference Methods

Author: J.W. Thomas

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 451

ISBN-13: 1489972781

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What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible.

Finite Difference Computing with Exponential Decay Models
Finite Difference Computing with Exponential Decay Models

Author: Hans Petter Langtangen

Publisher: Springer

Published: 2016-06-10

Total Pages: 210

ISBN-13: 3319294393

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This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization. The pedagogical strategy is to use one case study – an ordinary differential equation describing exponential decay processes – to illustrate fundamental concepts in mathematics and computer science. The book is easy to read and only requires a command of one-variable calculus and some very basic knowledge about computer programming. Contrary to similar texts on numerical methods and programming, this text has a much stronger focus on implementation and teaches testing and software engineering in particular.

Finite Difference Computing With PDEs
Finite Difference Computing With PDEs

Author: Hans Petter Langtangen

Publisher:

Published: 2020-10-08

Total Pages: 520

ISBN-13: 9781013268502

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This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.

Finite Difference Computing with PDEs
Finite Difference Computing with PDEs

Author: Hans Petter Langtangen

Publisher: Springer

Published: 2017-06-14

Total Pages: 610

ISBN-13: 9783319554556

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This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology. This book is open access under a CC BY license.

Numerical Solution of Differential Equations
Numerical Solution of Differential Equations

Author: Zhilin Li

Publisher: Cambridge University Press

Published: 2017-11-30

Total Pages: 305

ISBN-13: 1107163226

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A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.

Finite Difference Computing with Pdes
Finite Difference Computing with Pdes

Author: Andy Flair

Publisher:

Published: 2022-09-27

Total Pages: 0

ISBN-13: 9781639892037

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An equation that relates to one or more functions with its derivatives is called a differential equation. A partial differential equation (PDE) is a type of differential equation, in which the equation consists of unknown multi variables with their partial derivatives. This is a special case of an ordinary differential equation. There is a large amount of modern mathematical and scientific research on methods for numerically approximating solutions of particular PDEs using computers. These are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives. Finite difference computing is one of the most widely used methods for solving PDEs. This book outlines the processes and applications of finite difference computing with PDEs in detail. The topics included herein on finite difference computing with PDEs are of utmost significance and bound to provide incredible insights to readers. The book is appropriate for students seeking detailed information in this area as well as for experts.

Numerical Solution of Partial Differential Equations by the Finite Element Method
Numerical Solution of Partial Differential Equations by the Finite Element Method

Author: Claes Johnson

Publisher: Courier Corporation

Published: 2012-05-23

Total Pages: 290

ISBN-13: 0486131599

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An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.