Numerical Solution of Differential Equations: Introduction to Finite Difference and Finite Element Methods

by Zhilin Li, Zhonghua Qiao, Tao Tang

Overview

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® codes, all available online.

Product Details

ISBN-13:	9781107163225
Publisher:	Cambridge University Press
Publication date:	11/30/2017
Pages:	300
Product dimensions:	6.97(w) x 10.00(h) x 0.71(d)

About the Author

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.

Table of Contents

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.

Editorial Reviews

'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, Choice

From the Publisher