Page 194 - Schaum's Outline of Differential Equations
P. 194
CHAP. 19] NUMERICAL METHODS FOR SOLVING DIFFERENTIAL EQUATIONS 177
MODIFIED EULER'S METHOD
This is a simple predictor-corrector method that uses Euler's method (see Chapter 18) as the predictor
and then uses the average value of y' at both the left and right end points of the interval \x n, x n + J
(n = 0, 1,2,...) as the slope of the line element approximation to the solution over that interval. The resulting
equations are:
predictor:
corrector:
+ 1 . It then follows from Eq. (19.2)
For notational convenience, we designate the predicted value of y n + 1 by py n
that
The modified Euler's method becomes
predictor:
corrector:
RUNGE-KUTTA METHOD
where
This is not a predictor-corrector method.
ADAMS-BASHFORTH-MOULTON METHOD
predictor:
corrector:
MILNE'S METHOD
predictor:
corrector:
