http://worldcat.org/entity/work/id/865580064

Numerical analysis of partial differential equations

BA balanced guide to the essential techniques for solving elliptic partial differential equations /b iNumerical Analysis of Partial Differential Equations/i 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:/ ulli The mathematical theory of elliptic PDEs/ /lili Numerical linear algebra/ /lili Time-dependent PDEs/ /lili Multigrid and domain decomposition/ /lili PDEs posed on infinite domains/ /li/ul 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, iNumerical Analysis of Partial Differential Equations/i 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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