Crank—Nicholson finite difference approximation

Denoting the solute species in a binary system by subscripts 1 and 2, the Crank-Nicholson finite difference approximation for... [Pg.38]

When faster reactions are dealt with, it may be profitable to remove the At/Ay2 < 0.5 condition and use an implicit method such as the Crank-Nicholson method.15 17 The finite difference approximation is then applied at the value of t corresponding to the middle of the j to j + 1 interval, leading to... [Pg.124]

Traditional finite difference methods [55, 81] for solving time-dependent second-degree partial differential equations (such as modified diffusion equation) include forward time-centered space (ETCS), Crank-Nicholson, and so on. For time-independent second-degree partial differential equations such as Poisson-Boltzmann equation, finite difference equations can be written after discretizing the space and approximating derivatives by their finite difference approximations. For space-independent dielectric constant, that is, E(r) = e, a tridiagonal matrix inversion needs to be carried out in order to obtain a solution for tp for a given/. [Pg.315]

Ehrlich (El) uses the Crank-Nicholson (C16) finite-difference procedure for the integration of the diffusion equation, with a three-point approximation of the space derivatives on either side of the moving... [Pg.136]