In this chapter, we will develop FD and FDTD solvers for a sequence of PDEs of increasing complexity. We will begin with the one-dimensional (1-D) wave equation, and then we will consider Laplace's equation with two spatial dimensions, Maxwell's equations for two-dimensional (2-D) problems, and the full system of three-dimensional (3-D) Maxwell's equations. Algorithm stability and accuracy will be analyzed, and several types of postprocessing will be developed to extract useful physical quantities from computed field solutions. Comprehensive references on the FDTD method include.