Finite difference schemes and partial differential equations /

The greater part of this book is devoted to material on time-dependent linear (i.e., hyperbolic and parabolic) equations and systems. Three introductory chapters on elliptic equations and systems are designed to prepare the student to go on to more advanced treatment elsewhere. (A most serious omission is not indicating specific references.) Automated grid generation and variable grids are not treated, nor is there any mention of finite element methods. What the author does do, and well, is offer a clear, unified treatment (with numerous examples and exercises) of the convergence, consistency, and stability of difference schemes, and their orders of accuracy. There are chapters on the basic theory of well-posed initial value and initial boundary-value problems as well. In addition, three appendixes offer necessary background material from matrix and vector analysis, real analysis, and complex analysis. Recommended for graduate students in applied mathematics and engineering. -R. J. Wernick, San Francisco State University