Derivation via Numerical Integration  Alternative Derivations of Euler's  Alternative Derivations of Euler's

Derivation via Taylor's Theorem

In Section (5.4), the derivation of Euler's method using a Taylor expansion was only a side comment away. Recall Taylor's expansion,

for some  . Euler's method is derived from the above equation by chopping off the final term and recognizing that y'(t) = f(t,y(t)) since y(t) is assumed to satisfy the differential equation:

 

Wed Oct 28 11:42:13 EST 1998