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

A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.

Zhilin Li (Author), Zhonghua Qiao (Author), Tao Tang (Author)

9781316615102, Cambridge University Press

Paperback / softback, published 30 November 2017

300 pages, 57 b/w illus. 55 exercises
24.6 x 17.4 x 1.5 cm, 0.6 kg

'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

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.

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.

Subject Areas: Maths for engineers [TBJ], Numerical analysis [PBKS], Differential calculus & equations [PBKJ]