# L-28 MCS 471 Wed 26 Oct 2022 : eulerexpmod.jl

# experiments with the modified Euler's method 
# on the test equation y' = y, y(0) = 1 

using Printf

"""
    modeulerexp(n::Int64,verbose::Bool=true)

The Modified Euler's method with 
n evaluations on the interval [0,1] on 
the test equation y' = y, y(0) = 1.
"""
function modeulerexp(n::Int64,verbose::Bool=true)
    h = 1.0/n
    if verbose
        println("  i   x       predict      correct        exact       error")
    end
    y0 = 1.0
    y1 = 1.0
    for i=1:n
        x = i*h
        y = (1.0+h)*y0
        y1 = y0 + h*(y0 + y)/2.0
        exact = exp(x)
        if verbose
            stri = @sprintf("%3d", i)
            strx = @sprintf("%.2f", x)
            stry = @sprintf("%.6e", y)
            stry1 = @sprintf("%.6e", y1)
            strexp = @sprintf("%.6e", exact)
            strerr = @sprintf("%.2e", abs(y1-exact))
            println("$stri  $strx  $stry  $stry1  $strexp  $strerr")
        end
        y0 = y1
    end
    return y1
end

"""
Runs the function eulerexp.
"""
function main()
    modeulerexp(10)
    println("Running for n = 10^i, i=1:6 :")
    exact = exp(1.0)
    for i=1:6
        y = modeulerexp(10^i, false)
        stri = @sprintf("%8d", 10^i)
        stry = @sprintf("%.13e", y)
        strerr = @sprintf("%.2e", abs(y-exact))
        println("$stri  $stry  $strerr")
    end
end

main()