## Numerical Solution of Partial Differential Equations

Finite Difference Methods

Author: Gordon D. Smith

Publisher: Oxford University Press

ISBN: 9780198596509

Category: Mathematics

Page: 337

View: 4333

Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.
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## Numerical Analysis of Partial Differential Equations Using Maple and MATLAB

Author: Martin J. Gander,Felix Kwok

Publisher: SIAM

ISBN: 1611975301

Category: Science

Page: N.A

View: 9753

This book provides an elementary yet comprehensive introduction to the numerical solution of partial differential equations (PDEs). Used to model important phenomena, such as the heating of apartments and the behavior of electromagnetic waves, these equations have applications in engineering and the life sciences, and most can only be solved approximately using computers. Numerical Analysis of Partial Differential Equations Using Maple and MATLAB provides detailed descriptions of the four major classes of discretization methods for PDEs (finite difference method, finite volume method, spectral method, and finite element method) and runnable MATLAB® code for each of the discretization methods and exercises. It also gives self-contained convergence proofs for each method using the tools and techniques required for the general convergence analysis but adapted to the simplest setting to keep the presentation clear and complete. This book is intended for advanced undergraduate and early graduate students in numerical analysis and scientific computing and researchers in related fields. It is appropriate for a course on numerical methods for partial differential equations.
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## Numerical Solution of Elliptic and Parabolic Partial Differential Equations with CD-ROM

Author: John A. Trangenstein

Publisher: Cambridge University Press

ISBN: 0521877261

Category: Mathematics

Page: 635

View: 6571

Theory, methods and software for elliptic (steady-state) and parabolic (diffusion) partial differential equations, plus linear algebra and error estimators.
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## Partial Differential Equations with Numerical Methods

Publisher: Springer Science & Business Media

ISBN: 3540887059

Category: Mathematics

Page: 262

View: 4329

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

Author: Claes Johnson

Publisher: Courier Corporation

ISBN: 0486131599

Category: Mathematics

Page: 288

View: 5232

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.
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## Numerical Methods for Nonlinear Partial Differential Equations

Author: Sören Bartels

Publisher: Springer

ISBN: 3319137972

Category: Mathematics

Page: 393

View: 722

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
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## Numerical solution of partial differential equations

with exercises and worked solutions

Author: Gordon D. Smith

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 179

View: 800

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## Numerical methods for partial differential equations

Author: Gwynne Evans,Jonathan M. Blackledge,Peter Yardley

Publisher: Springer Verlag

ISBN: 9783540761259

Category: Mathematics

Page: 290

View: 4326

The subject of partial differential equations holds an exciting place in mathematics. Inevitably, the subject falls into several areas of mathematics. At one extreme the interest lies in the existence and uniqueness of solutions, and the functional analysis of the proofs of these properties. At the other extreme lies the applied mathematical and engineering quest to find useful solutions, either analytically or numerically, to these important equations which can be used in design and construction. The book presents a clear introduction of the methods and underlying theory used in the numerical solution of partial differential equations. After revising the mathematical preliminaries, the book covers the finite difference method of parabolic or heat equations, hyperbolic or wave equations and elliptic or Laplace equations. Throughout, the emphasis is on the practical solution rather than the theoretical background, without sacrificing rigour.
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## Numerical Partial Differential Equations: Finite Difference Methods

Author: J.W. Thomas

Publisher: Springer Science & Business Media

ISBN: 1489972781

Category: Mathematics

Page: 437

View: 8463

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.
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## The Numerical Solution of Ordinary and Partial Differential Equations

Author: Granville Sewell

Publisher: World Scientific

ISBN: 9814635111

Category: Mathematics

Page: 348

View: 6968