I have a small system of stiff ODEs describing a chemical reaction. The right-hand side is quite complicated, as well as the Jacobian. This equation will be solved many times with different initial conditions. Given that I've already selected a stiffness-oriented method, is it realystic to create more effective code than some existing solver? For example, is it worth trying to invest into optimizing LU-decomposition for my small system by loop unrolling, or whatever?
In this thread some general ideas are given, but maybe there are some tips about stiff ODE solution?
Update: there are only three equations. I'm using Fortran and compared the efficiency of RADAU (implicit RK), RODAS (Rosenbrock) and DLSODE (BDF method) codes. RODAS seems to work a bit faster.