ABSTRACT
As !J.t -+ 0 and tu -+ 0, Eq. (10.124) approaches!, + ufx = rxfxX" Consequently, Eq. (10.123) is a consistent approximation of the convection-diffusion equation, Eq. (10.104). From a von Neumann stability analysis, the amplification factor G is
IG = (10.125) I + 2d(l - cos e) + Ie sin e
The term (I - cos e) is ::: 0 for all values of e= (km tu). Consequently, the denominator of Eq. (10.125) is always::: I, IGI :::: I for all values of c and d, and Eq. (10.123) is unconditionally stable. The BTCS approximation of the convection-diffusion equation is consistent and unconditionally stable. Consequently, by the Lax Equivalence Theorem it is a convergent approximation of that equation.
