The Mathematics of Financial Modelingand Investment Management

9-DifferntEquations Page 253 Wednesday, February 4, 2004 12:51 PM

Differential Equations and Difference Equations 253

EXHIBIT 9.2 Numerical Solution of the Equation f ′′+ f = 0 with the Euler

Approximation

= hyi

1



k 2 ()+ ---h 1

2

= –h xi^1

h 2 ()+ ---k 1

2

= hyi

1



k 3 ()+ ---h 2

2

1



h 3 = –h xi()+ ---k 2

2

k 4 = hyi[ ()+ h 3 ]