 Aside

Assume a continuum problem described by a PDE is to be computed using a numerical scheme based upon a uniform computational grid and a one-step, constant step-size, "M" grid point, integration algorithm, either implicit or explicit.Then if formula_1 and formula_2, such a scheme can be described by

In other words, the solution formula_4 at time formula_5 and location formula_6 is a linear function of the solution at the previous time step formula_7.We assume that formula_8 determines formula_4 uniquely.