Plotting Time Step Range for Temperature Profiles in Matlab/Mathematica

[Dustinsfl]

Using this series approximation, plot the temperature profiles on the same set of axes for a range of time steps in the dimensionless time interval $t\in [0,4]$ in order to visualize the process.
$$
\begin{alignat*}{3}
T(x,t) & = & 1.7624\cos(0.86x)e^{-0.86^2t} - 0.1638\cos(3.426x)e^{-3.426^2t} + 0.476\cos(6.437x)e^{6.437^2t}\\
& - & 0.0218\cos(9.529x)e^{-9.529^2t} + 0.0124\cos(12.645x)e^{-12.645^2t} - 0.0080\cos(15.771x)e^{-15.771^2t}\\
& + & 0.0055\cos(18.902x)e^{-18.902^2t} - 0.0041\cos(22.036x)e^{-22.036^2t} + 0.0031\cos(25.172x)e^{-25.172^2t}\\
& - & 0.0025\cos(38.31x)e^{-28.31^2t}
\end{alignat*}
$$
How can I do this in Matlab or Mathematica?

 

[Ackbach]

In Mathematica, you could do something like this:

f[x_,t_]=your_function
PlotOne=Plot[... at t=0]
PlotTwo=Plot[... at t=0.5]
PlotThree=Plot[... at t=1]
.
.
.
Show[PlotOne,PlotTwo,PlotThree].

 

[Dustinsfl]

PlotOne = Plot[f[x,0],{x,-10,10}]

Like this?

 

[Ackbach]

Exactly. Just make sure your $x$ range corresponds to the region of interest for the problem.

 

[alphy]

In order to plot the temperature profiles for a range of time steps in Matlab or Mathematica, you can follow these steps:

1. Define the time interval and the time step range: Set the dimensionless time interval $t \in [0,4]$ and define a range of time steps, such as $dt = [0.1, 0.2, 0.5, 1, 2]$.

2. Create a vector for the x-axis: Use the linspace function in Matlab or the Range function in Mathematica to create a vector for the x-axis with a range of values, such as $x = [0:0.1:10]$.

3. Create a matrix for the temperature profiles: Use the provided series approximation formula to calculate the temperature profiles for each time step and store them in a matrix, where each column represents a different time step.

4. Plot the temperature profiles: Use the plot function in Matlab or the Plot function in Mathematica to plot the temperature profiles on the same set of axes, using the x-axis vector and the temperature profile matrix.

5. Add a legend and labels: Add a legend to the plot to distinguish between the different time steps, and add labels for the x-axis and y-axis to provide context for the plot.

6. Adjust the plot settings: You can adjust the plot settings, such as the line colors and styles, to make the plot more visually appealing and easier to interpret.

By following these steps, you should be able to plot the temperature profiles for a range of time steps in Matlab or Mathematica and visualize the process.