' - - File: XIIIa ; IVP for first order differential equation: X'(t) = F{t,x}

F{t,x} = 1 + x^2                                             ' Exact Solution: Y(x) = Tan[x + Atan[0.5] ]
to = 0  : tf = 1.1  :  xo = 0.5
IVP[F, {to, tf, xo}{1.1, 0.0001}]
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' Test Case: the value at  t = 1.10
'    Solution: X{t} = Tan[t + ATan[.5]} ; x{1.1} = 1.398828425 by calculator.
'    X(1.10) = 139.902 with TOL = 0.0001.
'    At an increase of 0.0001, we get accuracy to 7 places--20 fold increase in time.
'    This is NOT necessary for a qualitative graphical analysis of the solution.
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' Since the Tan[90 degrees] is undefined, the IVP algorithm found Tan[89.50]. (degrees)

