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

# Applies the backward euler on the stiff problem.
# y' = 10*(1-y), y(0) = 0.5, y(x) = 1 - exp(-10*x)/2.

using Printf

function backwardEuler(n::Int)
    h = 100.0/n
    y0 = 0.5
    println("step :    x     :     approximation      : error")
    for i=1:n 
        x = i*h
        y1 = (y0 + 10*h)/(1 + 10*h)
        y0 = y1
        exact = 1 - exp(-10*x)/2
        err = abs(y1 - exact)
        scnt = @sprintf("%4d", i)
        strx = @sprintf("%.2e", x)
        ssol = @sprintf("%.16e", y1)
        serr = @sprintf("%.2e", err)
        println("$scnt : $strx : $ssol : $serr")
    end
end

function main()
    println("Backward Euler on y' = 10*(1-y), y(0) = 0.5 ...")
    backwardEuler(10)
end

main()