II. FINITE DIFFERENCE METHOD 1 Difference formulae

y
0.0 0.1 0.2 0.3 0.4 0.5
−y’’+(x^2−1)y=0, y(−3)=e^(−9/2),y(−3)=e^(−9/2)
−3 −2 −1 0 1 2 3
Figure 3: The difference method applied to the harmonic oscillator ¡y ′′ (x)+(x 2 ¡
1)y(x) = 0 with Dirichlet conditions y(¡3) = y(3) = e −4.5 .
y
−0.3 −0.2 −0.1 0.0 0.1 0.2 0.3
x
y’’(x)+x^2y(x)=sin(x), y(−4*pi)=0, y(4*pi)=0
−10 −5 0 5 10
Figure 4: The difference method applied to the forced harmonic oscillator y ′′ (x)+
x 2 y(x) = sin(x) with Dirichlet conditions y(¡4π) = 0 , y(4π) = 0.
x
10