written RK solving same equation with different graphs

[acbshinn]

Hello all! I'm writing a simple Runge-Kutta solver and seem to be running into issues.

import numpy as np
import matplotlib.pyplot as plt


y0=1

"The amplitude function derivative, a complex exponential"
def amp(x,s):
    return .4j*x

"An explicit form of the same derivative"
def expamp(x,s):
    return .4j*np.exp(.4j*s)

"A simple Runge-Kutta solving algorithm"
def rk4(f,  t):
    y=np.zeros(len(t), dtype=complex) "I feel like the problem originates here"
    y[0]=y0 "Initial Value"
    h=t[1]-t[0] "Iteration time step"
    for i in range(0, len(t)-1):
        K1=(f(y[i], t[i]))
        K2=(f(y[i]+K1/2, t[i]+h/2))
        K3=(f(y[i]+K2/2, t[i]+h/2))
        K4=f(y[i]+K3, t[i]+h)
        y[i+1]=y[i]+h*(K1+K2+K3+K4)/6
        
    return y

"The Analytical Solution"    
def anal(t):
    return np.exp(.4j*t)

time=np.linspace(0,100,1000)
sol=rk4(amp, time)
exp=rk4(expamp, time)
an=anal(time)
plt.plot(time, an, 'b-', label='analytical')
plt.plot(time, exp, 'g.-', label='explicit RK solved')
plt.plot(time, sol, 'k--', label='RK Solved implicit')
plt.ylabel('probability')
plt.xlabel('time')
plt.legend()

Then I plotted the implicit, explicit, and analytical solutions and while the explicit and analytical solutions both show full oscillatory behavior, the implicitly solved one shows something similar to a damped harmonic oscillator(waves decaying eventually down to zero) (I can't figure out how to put the image on here, my school computer won't let me transfer images to get a URL)
I'm sure there's something in some call somewhere that's telling it to do this, but I'm having trouble finding where. Feel free to just copy/paste. I think you need pyplot and numpy the way I've written it. Can anyone shed any light on this for me?

Thank you all so much for your help!

[Gribouillis]

The explicit solution is very far from the analytical solution. Why is that so?
Replacing line 25 with

        y[i+1]=y[i]+h*(K1+2*(K2+K3)+K4)/6

gives a much better explicit solution, following the formula given by Wikipedia.

In fact the other formulas are also wrong. I get good results with both methods and

        K1=(f(y[i], t[i]))
        K2=(f(y[i]+h*K1/2, t[i]+h/2))
        K3=(f(y[i]+h*K2/2, t[i]+h/2))
        K4=f(y[i]+h*K3, t[i]+h)
        y[i+1]=y[i]+h*(K1+2*(K2+K3)+K4)/6