Problem

Edit your solver so that it uses an adaptive procedure. This can be done by choosing an appropriate step length $k_n$,

$$k_n = \frac{\textrm{TOL}}{S_c(t)\cdot R_n}$$ (6)

where $\textrm{TOL}$ is your error tolerance, $S_c(t)$ the stability factor, and $R_n$ the residual. A more useful approximation is to use $R_{n-1}$ instead of $R_n$. In this session, you will assume that $S_c(t) = 1$.

Apply your adaptive solver to equation (3).
Question 3 Is there a change in the timestep? Explain this.