Numerical Solution of Differential Equations

Erscheinungsjahr 2017
ISBN: 978-1-316-61510-2
Verlag: Cambridge University Press

Buch, Englisch, 293 Seiten, Format (B × H): 189 mm x 246 mm, Gewicht: 596 g

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.

Autoren/Hrsg.

Li, Zhilin

Qiao, Zhonghua

Tang, Tao

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis

Inhaltsverzeichnis

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.

Über Autor(innen)

Li, Zhilin
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.

Tang, Tao
Tao Tang is a Professor in the Department of Mathematics at South University of Science and Technology, China.

Qiao, Zhonghua
Zhonghua Qiao is an Assistant Professor in the Department of Applied Mathematics, Hong Kong Polytechnic University.