Finite Difference Schemes and Partial Differential Equations

This book combines practical aspects of implementation with theoretical analysis of finite difference schemes and partial differences schemes. There is a thorough discussion of the concepts of convergence, consistency, and stability for time-dependent equations. The von Neumann analysis of stability is developed rigorously using the methods of Fourier analysis. Fourier analysis is used throughout the text, providing a unified treatment of the basic concepts and results. A complete proof of the Lax-Richtmyer theorem for equations with constant coefficients is included.