To my MEC2010 group members,

The test function you should implement in your expression is as follows:

$$\theta(i,j)=\varepsilon \cdot \sin \bigg( \frac{ij\pi}{n_{x}} \bigg)$$

The test case was the diffusion (heat) equation:

$$\frac{\partial U}{\partial t}=\kappa\frac{\partial^{2}U}{\partial x^2}$$

In your response, you need to discuss the conditions that ensure numerical stability and produce a plot using meshgrid() to show the stable and unstable cases respectively.

Email me if further clarification is required.