Clear[a,b,h,L,x,y,k1,k2,k3,k4];
a=0;
b=1;
y[0]=1;
h=0.5;
L=(b-a)/h;
Do[x[n]=n*h,{n,0,L}]​​(*y'[x]==-y[x]*)​​f[x_,y_]=-y;​​Do​​k1=h*f[x[n],y[n]],​​k2=h*fx[n]+
h
2
,y[n]+
k1
2
,​​k3=h*fx[n]+
h
2
,y[n]+
k2
2
,​​k4=h*f[x[n]+h,y[n]+k3],​​y[n+1]=y[n]+
k1
6
+
k2
3
+
k3
3
+
k4
6
,​​{n,0,L};