Numerical solution of partial differential equations

Author: (English) Morton
Publisher:
Publish Date: 2006-01-01
Features: This is a highly acclaimed textbook on numerical techniques for partial differential equations, adopted by several renowned universities abroad as a teaching material. The book explains standard numerical methods and techniques for solving partial differential equations and incorporates the latest developments in the field. It thoroughly analyzes the properties of various methods, rigorously discusses stability issues, and provides examples and exercises suitable for different levels. The book is well-organized, concise, and clear. It serves as the preferred introductory textbook for students in mathematics, engineering, and computer science to learn numerical methods for partial differential equations. Partial differential equations are the primary tools for constructing mathematical models in science, engineering, and other fields. Generally, these models require numerical methods for solution. The book provides a concise introduction to standard numerical techniques. Common finite difference methods, finite element methods, finite volume methods, modified equation analysis, symplectic integration schemes, convection-diffusion problems, multigrid methods, and conjugate gradient methods are introduced with simple examples of parabolic, hyperbolic, and elliptic equations. 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 offers examples and exercises of varying difficulty. It can be used as a textbook for undergraduate students in mathematics, engineering, and computer science, as well as a reference for engineers, technicians, and applied workers.