Application to a Simple Example ODE

A simple example serves to illustrate the use of Rosenbrock, using the ode 

This is of interest because it contains i, so that we must use both fy and ft, both equal to unity. Applying the ROS2 variant to this (see Appendix A for the coefficient values), (4.70) (now for a single variable y) translates to the two equations 

In publications providing Rosenbrock coefficients such as [100,347], there appear alternative coefficients, hatted , such as etc. These always provide another variant with an order smaller by one than the one used. The purpose of this is that the difference between the two forms provides an (over)estimate of the error. The practice is not followed in this book, as we are generally mainly interested in the error order. So these alternative, lower-order coefficients are not included in Appendix A. 

---