This code is python progaming code about solve "Kirchoff's law" about diffrent way of time scheme. I think this code will be plot a grapgh seems like cosine function. But those code ara not same as cosine function, and It's converging at zero. Can you fix the code and it seems like a cosine function?

import numpy as np

import matplotlib.pyplot as plt

# Constants

V $=1$ # Voltage $($V$)$

LC $=1$ # Inductance$-$Capacitance product $($F$*$H$)$

delta$\_$t $=0\mathrm{.}1$ # Time step $($s$)$

num$\_$steps $=500$ # Number of time steps

# Initialize arrays

time $=$ np$.$zeros$($num$\_$steps$)$

voltage$\_$values $=\{$

'Crank$-$Nicolson': np$.$zeros$($num$\_$steps$),$

'Runge$-$Kutta': np$.$zeros$($num$\_$steps$),$

'Euler$-$Explicit': np$.$zeros$($num$\_$steps$),$

$\}$

# Initial condition

voltage$\_$values$[\text{'}$Crank$-$Nicolson'$][0]=$ V

voltage$\_$values$[\text{'}$Runge$-$Kutta'$][0]=$ V

voltage$\_$values$[\text{'}$Euler$-$Explicit'$][0]=$ V

# Numerical schemes

def crank$\_$nicolson$($prev$\_$v$,$ LC$,$ delta$\_$t$)$:

return $(2*$ prev$\_$v $+2*$ V $*$ delta$\_$t $/$ LC$)/(2+2*$ delta$\_$t $/$ LC$)$

def runge$\_$kutta$($prev$\_$v$,$ LC$,$ delta$\_$t$)$:

k$1=-($prev$\_$v $/$ LC$)$

k$2=-(($prev$\_$v $+$ k$1*$ delta$\_$t$/2)/$ LC$)$

k$3=-(($prev$\_$v $+$ k$2*$ delta$\_$t$/2)/$ LC$)$

k$4=-(($prev$\_$v $+$ k$3*$ delta$\_$t$)/$ LC$)$

return prev$\_$v $+($delta$\_$t $/6)*($k$1+2*$k$2+2*$k$3+$ k$4)$

# Euler$-$Explicit method is straightforward

for t in range$(1,$ num$\_$steps$)$:

time$[$t$]=$ t $*$ delta$\_$t

voltage$\_$values$[\text{'}$Crank$-$Nicolson'$][$t$]=$ crank$\_$nicolson$($voltage$\_$values$[\text{'}$Crank$-$Nicolson'$][$t$-1],$ LC$,$ delta$\_$t$)$

voltage$\_$values$[\text{'}$Runge$-$Kutta'$][$t$]=$ runge$\_$kutta$($voltage$\_$values$[\text{'}$Runge$-$Kutta'$][$t$-1],$ LC$,$ delta$\_$t$)$

voltage$\_$values$[\text{'}$Euler$-$Explicit'$][$t$]=$ voltage$\_$values$[\text{'}$Euler$-$Explicit'$][$t$-1]-($voltage$\_$values$[\text{'}$Euler$-$Explicit'$][$t$-1]/$ LC$)*$ delta$\_$t

# Plotting

plt$.$figure$($figsize$=(10,6))$

for scheme, values in voltage$\_$values.items$()$:

plt$.$plot$($time$,$ values, label$=$scheme$)$

plt$.$xlabel$(\text{'}$Time $($s$)\text{'})$

plt$.$ylabel$(\text{'}$Voltage $($V$)\text{'})$

plt$.$title$(\text{'}$Voltage$-$Time for Different Numerical Schemes'$)$

plt$.$legend$()$

plt$.$grid$($True$)$

plt$.$show$()$