Question

Solve the heat equation initial$-$boundary$-$value problem:

$u_t=u_{}$

with the initial and boundary conditions:

$u(x,0)=3+cos(2x),u_x(0,t)=u_x(3,t)=0$

MATLAB Task

Using MATLAB, plot the solutions to the heat equation problem in two

different ways:

As surfaces $u(x,t)$ in three$-$dimensional space.

As functions of $x$ in the $x-u$ plane for various fixed values of $t.$

Investigation

In each case, investigate the behavior as $t,$ focusing on the steady$-$

state behavior.

Graduate Attribute Reflection Question

Reflect on the learning strategies you used in solving this problem and

exploring the MATLAB visualizations. Consider the following in your

reflection:

What challenges did you face in solving the heat equation and under$-$

standing the initial$-$boundary conditions?

$-$What resources or strategies helped you overcome these challenges?

How did the MATLAB visualizations of the heat equation solution

contribute to your understanding of the problem?

What learning strategies worked best for you in this task, and how

can you apply them to future problems?