Coverage of finite-difference approximations in section 9.3, Boundary-Value Problems: Numerical Methods (for ordinary differential equations), and of the method of lines in Section 9.6, Initial-Boundary-Value Problems, will require about three days.
The analysis of the resulting systems of ordinary differential equations is in part analytic, using the linear systems ideas of section 8.2, Constant-Coefficient, Homogeneous Systems, to estimate rates of decay, for example, and in part numerical, calling upon the initial-value solvers Euler, Heun, and RK4 of section 3.1, Numerical Methods, to find numerical approximations. Such estimates are compared with the results of the Fourier analysis in section 9.5.