Summary: GENERAL ERROR FORMULA
In general,
yn+1 = yn + h f(xn; yn); n = 0; 1; :::; N 1
Y (xn+1) = Y (xn) + h Y 0(xn) +
h2
2
Y 00( n)
= Y (xn) + h f(xn; Y (xn)) +
h2
2
Y 00( n)
with some xn n xn+1.
We will use this as the starting point of our discussion
of the error in Euler's method. In particular,
Y (xn+1) yn+1 = Y (xn) yn
+h [ f(xn; Y (xn)) f(xn; yn)]
+
h2
2
Y 00( n)

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa

Collections: Computer Technologies and Information Sciences