Numerical Solution of Differential Equations
Numerical Solution of Differential Equations
Zhonghua Qiao, Hong Kong Polytechnic University
Tao Tang, Southern University of Science and Technology, Shenzhen, China
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.
- Offers a concise and practical introduction to finite difference and finite element methods
- Well-tested MATLAB® codes are free to download
- Teaches students how to use computers to solve linear ODEs and PDEs in one and two dimensions
Reviews & endorsements
'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
Product details
November 2017Adobe eBook Reader
9781316730218
0 pages
0kg
57 b/w illus. 55 exercises
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
