ABSTRACT

Eq. (10.104). _

The solution to Eq: (10.104) is the function f(x, t). This function must satisfy an initial condition at t = O,f(x, 0) = F(x). The time coordinate has an unspecified (i.e, open) final value. Equation (10.104) is second order in the space coordinate x. Consequently, two boundary condition~ (BCs) are required. These BCs may be of th.7 Dirichlet type (i.e., specified values of f), the Neu~ann !ype (i.e., specified values ofIx), or the mixed type (i.e., specified combinations off andj~). The space coordinate x must be a closed physical domain.