# L-31 MCS 471 Wed 2 Nov 2022 : rk45exp.jl

# Using RK45 of the SciPy.integrate module on the test equation.

using SciPy
using Printf

println("Solving y\' = y, y(0) = 1 with SciPy.integrate.RK45")

testfun(t,y) = y
sol = SciPy.integrate.RK45(testfun, 0.0, (1.0,), 1.0, rtol=1.0e-8)

println("step :     t    :    h     :           y            :  error")

stepcnt = 0
while sol.status != "finished"
    sol.step()
    global stepcnt = stepcnt + 1
    scnt = @sprintf("%4d", stepcnt)
    step = @sprintf("%.2e", sol.step_size)
    tval = @sprintf("%.2e", sol.t)
    soly = @sprintf("%.16e", sol.y[1])
    err = abs(sol.y[1] - exp(sol.t))
    serr = @sprintf("%.2e", err)
    println("$scnt : $tval : $step : $soly : $serr")
end