Two-dimensional heat equation in 3d graph - python

Question

I have a problem, i.e. I don't know how to draw a 3D graph in python according to the given equation that I calculated. The graph is limited to x (from 0 to 1) and to y (from 0 to 2). n is a variable that goes from 1 to infinity. the sum of all solutions must be plotted on the 3d graph. I am attaching a picture of the equation and what the graph should look like. what graph should look like

equation

Can you help me please?

I tried to create this graph in python, geogebra, mathlab,... but i don't know how. I need this for the project assignment and I only have two days more.

Answer 1

import numpy as np
import matplotlib.pyplot as plt

# Heat equation at coordinates x and y
# Will add up first n terms of summation
def heat_eq(x, y, n):
    total = 0

    for i in range(1, n + 1):
        total += (
            np.sin(i * np.pi * x)
            * -8
            / (i**3 * np.pi**3 * np.sinh(2 * i * np.pi))
            * np.sin((2 - y) * i * np.pi)
        )

    return total


# 1-D arrays of x and y coordinates
x = np.arange(0, 1, 0.1)
y = np.arange(0, 2, 0.1)

# Turn x,y into 2D coordinates
y, x = np.meshgrid(y, x, indexing="ij")

# Get heat equation values at x,y coordinates. n = 100 seems sufficient for convergence
z = heat_eq(x, y, 100)

# Basic 3D plotting
fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(projection="3d")
ax.plot_surface(x, y, z, linewidth=0, antialiased=True, cmap="coolwarm")