Numerical Solution of Partial Differential Equations: Second Edition

Author: (English) Morton
Publisher:
Publication Date: 2006-01-01
Features: This is a highly acclaimed textbook on numerical techniques for partial differential equations, adopted by several renowned universities abroad, including Oxford University, University of Maryland, North Carolina State University, and others. The book covers standard numerical methods for solving partial differential equations while also providing the latest advancements in the field. It thoroughly analyzes the properties of various methods, rigorously discusses stability issues, and offers examples and exercises for different levels. The book is well-structured, concise, and clear, making it the ideal introductory textbook for students in mathematics, engineering, and computer science to learn numerical methods for partial differential equations. Partial differential equations serve as the primary means of constructing mathematical models in science, engineering, and other fields. Generally, these models require numerical methods for solution. This book provides a concise introduction to standard numerical techniques. Through simple examples of parabolic, hyperbolic, and elliptic equations, it introduces commonly used methods such as finite difference methods, finite element methods, finite volume methods, modified equation analysis, symplectic integration schemes, convection-diffusion problems, multiple networks, and conjugate gradient methods. Stability issues are addressed clearly and rigorously using the maximum principle, energy methods, and discrete Fourier analysis. The book comprehensively discusses the properties of these methods, accompanied by typical graphical results, and provides examples and exercises of varying difficulty. It can serve as a textbook for undergraduate students in mathematics, engineering, and computer science, as well as a reference for engineers, technicians, and applied workers.