Page 181 - Schaum's Outline of Differential Equations

164 GRAPHICAL METHODS FOR SOLVING DIFFERENTIAL EQUATIONS [CHAP. 18

Fig. 18-9

Fig. 18-10

18.10. Give a geometric derivation of Euler's method.
Assume that y n = y(x n) has already been computed, so that y' n is also known, via Eq. (18.5). Draw a straight
line l(x) emanating from (x n, y n) and having slope y' n, and use l(x) to approximate y(x) on the interval [x n, x n+1] (see