' File XVIIIa                 4th Order DEQ

c1 = 0 : c2 = 0.3 : c3 = 1 : c4 = 1
xo = c1 + c3  : yo = c2 + c4  : zo = -c3  :  wo = -c4
to = 0  :  tf = 10

F{t,x,y,z,w} = y
G{t,x,y,z,w} = z
H{t,x,y,z,w} = w
R{t,x,y,z,w} = -z

IVP[F,G,H,R,{to,tf,xo,yo,zo,wo} {1.00, .05, 3}]

'  - - - - - - - - - - - Verification - - - - - - - - - - - - - -
X{t} = c1 + c2 *t + c3*Cos[t] + c4*Sin[t]
V<t> = <t, X, 0>

' Option: Translate the X{t} solution to "observe" the match.
tx = 0.10 : ty = 0 : tz = 0
U<t> = vTran[V,tx, ty,tz]
'Plot[U, {t,to,tf,200}]    

'NOTE: From prevous examples using overlays, recall that IVP uses a variable increment.
' So the Plot of vector U may not end at the same value as IVP plot. However, just change
' the 200 to increase (decrease) plot number of points.. This action does not distort vector
' U. Rather, the addition to (subtraction from) allows extended data points.

' Use Plot[V, {t, to, tf, 200}] and the markers to do an alternate test for validity.


