DDAPLUS Differential-algebraic

The DDAPLUS algorithm (Caracotsios and Stewart, 1985), updated here, is an extension of the DDASSL (Petzold, 1982) implicit integrator. DDAPLUS solves differential-algebraic equation systems of the form... 

Three examples are given here to demonstrate various capabilities of DDAPLUS. In the first example, DDAPLUS is used to solve a system of ordinary differential equations for the concentrations in an isothermal batch reactor.In the second example, the same state equations are to be integrated to a given time limit, or until one of the state variables reaches a given limit. The last example demonstrates the use of DDAPLUS to solve a differential-algebraic reactor problem with constraints of electroneutrality and ionization equilibria. 

Another common property of multireaction networks is stiffness, that is, the presence of kinetic steps with widely different rate coefficients. This property was pointed out by Curtiss and Hirschfelder (1952), and has had a major impact on the development of numerical solvers such as BASSE (Petzold 1983) and DDAPLUS of Appendix B. Since stiff equations take added computational effort, there is some incentive to reduce the stiffness of a model at the formulation stage this can be done by substituting Eq. (2.5-2b) or (2.5-3) for some of the reaction or production rate expressions. This strategy replaces some differential equations in the reactor model by algebraic ones to expedite numerical computations. 

This appendix explains how to use DDAPLUS to solve nonlinear initial-value problems containing ordinary differential equations with or without algebraic equations, or to solve purely algebraic nonlinear equation systems by a damped Newton method. Three detailed examples are given. 

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