ABSTRACT
PDEs the wave equation. Section 11.9 presents an introduction to the numerical solution of the wave equation.
The solution to Eqs. (11.6) and (11.7) is the function f(x, t). For Eqs. (11.6) and (11.7), this function must satisfy an initial condition at time t = 0, f(x, 0) = F(x). Equation (11.7) must also satisfy a second initial condition !rex, 0) = G(x). Since Eq. (I 1.6) is first order in space x, only one boundary condition can be applied. Since Eq. (I 1.7) is second order in space, it requires two boundary conditions. In both cases, these boundary conditions may be of the Dirichlet type (i.e., specified values off), the Neumann type (i.e., specified values ofIx), or the mixed type (i.e., specified combinations off and j,J The basic properties of finite difference methods for solving propagation problems governed by hyperbolic PDEs are presented in this chapter.
