An application of GRK4A

Problem E3 (stiff ODE) from Enright & Pryce was solved using the Kaps-Rentrop GRK4A parameters. The ODE’s are as follows:

 The IV’s are y1(0)=y2(0)=1, y3(0)=0. A tolerance of 1E-5 was used.

Application of the Rosenbrock Triple

The Rosenbrock triple was used to solve problem A3 from Enright & Pryce. The ODE’s are:









The initial values for all equations are 1. The Kaps-Rentrop variable step method was used, with an initial starting time of 1E-5. The solutions are plotted below.



The solutions for the equations have vastly varying settling times as noted in the plots. A zoomed-in view of the solution between times t=0 and 0.02 is shown below.



Equations y1 and y2 reach steady-state in less than 0.005 s, while y3 takes over 20 s to “settle down”. As noted earlier, such equations that have quantities with vastly varying settling times are referred to as “stiff” ODE’s. The more powerful the ODE solver, the quicker is the iterative process to converge at a solution for the entire time period of interest.