Page 213 - Schaum's Outline of Differential Equations
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196 SOLVING SECOND-ORDER DIFFERENTIAL EQUATIONS [CHAP. 20
The formulas that follow are for systems of two equations in standard form (20.1) Generalizations to
systems of three equations in standard form (20.2) or systems with four or more equations are straightforward.
EULER'S METHOD
RUNGE-KUTTA METHOD
where
ADAMS-BASHFORTH-MOULTON METHOD
predictors:
correctors:
Corresponding derivatives are calculated from System (20.1). In particular,
The derivatives associated with the predicted values are obtained similarly, by replacing y and z in Eq. (20.6)
with py and pz, respectively. As in Chapter 19, four sets of starting values are required for the
Adams-Bashforth-Moulton method. The first set comes directly from the initial conditions; the other three sets
are obtained from the Runge-Kutta method.
