Numerical Solution of Differential Equations
Introduction to Finite Difference and Finite Element Methods
Published on 30. November 2017
Book
Hardback
300 pages
978-1-107-16322-5 (ISBN)
Description
This introduction to finite difference and finite element methods is aimed at graduate students who need to solve differential equations. The prerequisites are few (basic calculus, linear algebra, and ODEs) and so the book will be accessible and useful to readers from a range of disciplines across science and engineering. Part I begins with finite difference methods. Finite element methods are then introduced in Part II. In each part, the authors begin with a comprehensive discussion of one-dimensional problems, before proceeding to consider two or higher dimensions. An emphasis is placed on numerical algorithms, related mathematical theory, and essential details in the implementation, while some useful packages are also introduced. The authors also provide well-tested MATLAB (R) codes, all available online.
Reviews / Votes
'The authors of this volume on finite difference and finite element methods provide a sound and complete exposition of these two numerical techniques for solving differential equations. The text is divided into two independent parts, tackling the finite difference and finite element methods separately. The parts offer a balanced mix of theory, application, and examples to offer readers a thorough introduction to the material. They utilize MATLAB programming to provide various codes illustrating the applications and examples. ... Overall, the textbook offers a solid introduction to finite difference methods and finite element methods that should be useful to graduate students in mathematics as well as to students in applied and interdisciplinary fields, such as engineering and economics, who need to solve differential equations numerically.' S. L. Sullivan, ChoiceMore details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Illustrations
Worked examples or Exercises; 12 Halftones, black and white; 45 Line drawings, black and white
Dimensions
Height: 250 mm
Width: 175 mm
Thickness: 21 mm
Weight
707 gr
ISBN-13
978-1-107-16322-5 (9781107163225)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Zhilin Li
Numerical Solution of Differential Equations
Introduction to Finite Difference and Finite Element Methods
E-Book
11/2017
Cambridge University Press
€36.99
Available for download
Zhilin Li | Zhonghua Qiao | Tao Tang
Numerical Solution of Differential Equations
Introduction to Finite Difference and Finite Element Methods
Book
11/2017
Cambridge University Press
€57.70
Shipment within 15-20 days
Zhilin Li | Zhonghua Qiao | Tao Tang
Numerical Solution of Differential Equations
Introduction to Finite Difference and Finite Element Methods
E-Book
11/2017
Cambridge University Press
€44.49
Available for download
Persons
Zhilin Li is a tenured full professor at the Center for Scientific Computation and the Department of Mathematics, North Carolina State University. His research area is in applied mathematics in general, particularly in numerical analysis for partial differential equations, moving interface/free boundary problems, irregular domain problems, computational mathematical biology, and scientific computing and simulations for interdisciplinary applications. Li has authored one monograph, The Immersed Interface Method, and also edited several books and proceedings. Zhonghua Qiao is an Assistant Professor in the Department of Applied Mathematics, Hong Kong Polytechnic University. Tao Tang is a Professor in the Department of Mathematics at South University of Science and Technology, China.
Content
1. Introduction; Part I. Finite Difference Methods: 2. Finite difference methods for 1D boundary value problems; 3. Finite difference methods for 2D elliptic PDEs; 4. FD methods for parabolic PDEs; 5. Finite difference methods for hyperbolic PDEs; Part II. Finite Element Methods: 6. Finite element methods for 1D boundary value problems; 7. Theoretical foundations of the finite element method; 8. Issues of the FE method in one space dimension; 9. The finite element method for 2D elliptic PDEs; Appendix. Numerical solutions of initial value problems; References; Index.