This text presents a comprehensive mathematical theory for elliptic, parabolic, and hyperbolic differential equations. It compares finite element and finite difference methods and illustrates applications of generalized difference methods to elastic bodies, electromagnetic fields, underground water pollution, and coupled sound-heat flows.

Ronghua Li, Zhongying Chen, Wei Wu

Preliminaries; two point boundary value problems; second order elliptic equations; fourth order and nonlinear elliptic equations; parabolic equations; hyperbolic equations; convection-dominated diffusion problems; applications.