An Example, the Birk-Perone System

There is an example program described in Appendix C, BPROS, applying Rosenbrock to the Birk-Perone system, in which we have both time-dependence and nonlinear equations. It is described in Chap. 2, pages 22-22. Equation (2.73), with boundary conditions, when semidiscretised using equal intervals in space, leads to the DAE system 

The last equation expresses the analytical solution for the time decay of the substrate. Here, then, we have selection matrix S as above (9.58), and the function F(T, C) is 

The above equation evaluates to a tridiagonal linear equation system, after some arrangement, 

Execution of the program BPROS shows that it works well, attaining a relative accuracy of about 10 4 in about 100 steps of ST = 0.01, both with ROS2 and ROWDA3, the latter being slightly better (but using about 50% more CPU time). 

---