ABSTRACT
Yn+1 = Yn + I1t In (7.104) Applying the explicit Euler method to the model ODE, ji + aji = 0, for which J(t, ji) = -aji, gives
I G=(I-a!1t) I For stability, IGI ::s 1. Thus,
-I ::s (I - a I1t) ::s 1
(7.105)
(7.106)
(7.107) The right-hand inequality is always satisfied for a I1t 2: 0. The left-hand inequality is satisfied only if
(7.108)
which requires that !1t ::s 2/a. Consequently, the explicit Euler method is conditionally stable.
