Problem

Modify your program from Problem 1 so that a new drop of substance $B$ is added at $x = (0.75, 0.5)$ every second, instead of just pouring it into the beaker. This can be accomplished by taking

$$f(x,t) = \left\{ \begin{array}{l} 20, \quad \mbox{if } \... ...rt < 0.1, \\ 0, \quad \mbox{otherwise}, \end{array} \right.$$ (6)

Also add a convective term corresponding to a magnetic stirrer at the bottom of the beaker, for example by taking

$$b(x,t) = 5(-(x_2-0.5), x_1-0.5).$$ (7)

Use a time step of size $k = 0.05$ and compute until time $T = 5$.

Check your answer: Compare your solution with the figure below, which shows the solution at time $t = 2.5$.