import Plots as plt

function odeRK4(f, y0, t)
    ns = length(t)-1
    y = zeros(ns+1)
    y[1] = y0
    
    for k in 1:ns
        h = t[k+1]-t[k]
        S1 = f(y[k],t[k])
        S2 = f(y[k]+0.5*h*S1, t[k]+0.5*h)
        S3 = f(y[k]+0.5*h*S2, t[k]+0.5*h)
        S4 = f(y[k]+    h*S3, t[k]+    h)
        y[k+1] = y[k] + h/6*(S1 + 2*S2 + 2*S3 + S4)
    end
        
    return y
end

function odeEE(f, y0, t)
    ns = length(t)-1
    y = zeros(ns+1)
    y[1] = y0
    
    for k in 1:ns
        h = t[k+1]-t[k]
        y[k+1] = y[k] + h*f(y[k],t[k])
    end
    
    return y
end

f(y,t) = -y

#----------------------

y0    = 1.0
tend  = 5.0
t     = LinRange(0,tend,11)

#----------------------

y_RK4 = odeRK4(f,y0,t)
y_EE  = odeEE(f,y0,t)

tt      = LinRange(0,tend,100)
y_Exact = exp.(-tt);


plt.resetfontsizes(); plt.scalefontsizes(1.5)
plt.plot(tt,y_Exact, label="exact", color="black")
plt.scatter!(t, y_RK4, label="RK4")
plt.scatter!(t, y_EE, label="EE", markershape=:utriangle)
plt.plot!(background_color_legend=nothing, foreground_color_legend=nothing)
plt.plot!(ylabel="y", xlabel="t")