Some Runge-Kutta schemes have the First-Same-As-Last (FSAL) property, that enables sharing a residual evaluation from one step to the next. It may not be possible to have this optimisation in our case because of the Dirichlet boundary conditions.
Ideas for later
Adaptive time-stepping with embedded Runge-Kutta methods or Richardson extrapolation
Linear multistep methods (Adam-Bashford, Adam-Moulton, Backward Difference Formula)
General linear methods
Numerical methods for differential-algebraic systems of equations (DAEs)
Leftover ideas after #985
TODO
Some Runge-Kutta schemes have the First-Same-As-Last (FSAL) property, that enables sharing a residual evaluation from one step to the next. It may not be possible to have this optimisation in our case because of the Dirichlet boundary conditions.
Ideas for later