|
|
|
The PDE is sampled at points \( (x_i,t_{n+\half}) \) (at the spatial mesh points, but in between two temporal mesh points). $$ \frac{\partial}{\partial t} u(x_i, t_{n+\half}) = \dfc\frac{\partial^2}{\partial x^2}u(x_i, t_{n+\half}) $$ for \( i=1,\ldots,N_x-1 \) and \( n=0,\ldots, N_t-1 \).
Centered differences in space and time: $$ [D_t u = \dfc D_xD_x u]^{n+\half}_i$$
|
|
|