Using this code as an example:

import numpy as np

import matplotlib.pyplot as plt

# Parameters

L $=1\mathrm{.}0$ # Length of the rod

alpha $=0\mathrm{.}1$ # Thermal diffusivity

T $=1\mathrm{.}0$ # Total time

dx $=0\mathrm{.}1$ # Spatial step

dt $=0\mathrm{.}01$ # Time step

# Discretization

x $=$ np$.$arange$(0,$ L $+$ dx$,$ dx$)$

Nx $=$ len$($x$)$

time$\_$steps $=$ int$($T $/$ dt$)$

# Initial condition

u $=$ np$.$ones$($Nx$)*100$ # Initial temperature: $100$C

# Finite difference method

for n in range$($time$\_$steps$)$:

u$\_$new $=$ np$.$copy$($u$)$

for i in range$(1,$ Nx $-1)$:

u$\_$new$[$i$]=$ u$[$i$]+$ alpha $*$ dt $/$ dx$**2*($u$[$i$-1]-2*$u$[$i$]+$ u$[$i$+1])$

# Apply boundary conditions

u$\_$new$[0]=100$ # Left end

u$\_$new$[-1]=0$ # Right end

u $=$ u$\_$new

# Visualization $($plot every $10$ steps$)$

if n $\%10==0$:

plt$.$plot$($x$,$ u$,$ label$=$f'Time $=\{$n$*$dt:$\mathrm{.}2$f$\}$s$\text{'})$

# Final plot settings

plt$.$title$(\text{'}$Temperature Distribution along the Rod'$)$

plt$.$xlabel$(\text{'}$Position along the rod $($m$)\text{'})$

plt$.$ylabel$(\text{'}$Temperature $($C$)\text{'})$

plt$.$legend$()$

plt$.$grid$()$

plt$.$show$()$

Complete the following tasks:

Initialize the temperature distribution along the rod.

Use the explicit finite difference method to update the temperature at each time step.

Apply the boundary conditions at each time step.

Visualize the temperature distribution at selected time intervals.