# Numerical Analysis of Partial Differential Equations

John Wiley & Sons, Aug 30, 2011 - Mathematics - 487 pages
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.

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### Contents

 Finite Difference 1 Mathematical Theory of Elliptic PDEs 45 Finite Elements 95 Numerical Linear Algebra 169 Spectral Methods 221 Evolutionary PDEs 291 Multigrid 345
 Domain Decomposition 369 Infinite Domains 420 Nonlinear Problems 441 Answers to Selected Exercises 471 References 477 Index 483 Copyright