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.

This book provides a unified and accessible introduction to the basic theory of finite difference schemes applied to the numerical solution of partial differential equations. Its objective remains to clearly present the basic methods necessary to perform finite difference schemes and to understand the theory underlying these schemes.