DASSL integrator

For our comparative evaluation of SAAM s Chu Berman (Qm and Berman, 1974) integrator (also referred to as model code 10 in SAAM and CONSAM) we will be considering as alternate integrators the Runge Kutta 4/2 integrator (Press et ai, 1987), the Bulirsch Stoer integrator (Press et al., 1987), and Petzold s DASSL integrator (Petzold, 1983). 

Write the appropriate driver routine to integrate the equations using either the DASSL [46] (DAE) or VODE (ODE) [49] software. You will need to iteratively solve for the laboratory-referenced molar fluxes N], N2 using a multidimensional root-finding routine, such as MNEWT / FDJAC [319], a Newton-Raphson scheme. 

The numerical solution is accomplished with a method-of-lines approach, using a control-volume spatial discretization. The time integration can be done using Dassl, which implements an implicit, variable-order, variable-step, method based on the BDF method [46],... 

Dassl, solves stiff systems of differential-algebraic equations (DAE) using backward differentiation techniques [13,46]. The solution of coupled parabolic partial differential equations (PDE) by techniques like the method of lines is often formulated as a system of DAEs. It automatically controls integration errors and stability by varying time steps and method order. 

Using the integration package DASSL (Petzolo, 1989) and implementing a routine in FORTRAN 90, we obtain the profiles in Figures 20.17 and 20.18. 

Therefore, powerful time integrators such as LIMFX, RADAU5 or DASSL [4, 6, 10] should be used to solve these complex systems. The advantage of the whole strategy is obvious the user only provides a suitable spatial mesh, the demanding time integration of the stiff system is automatically and adaptively done by a black-box solver. This first element of adaptivity is already quite popular. 

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