WHAT DDAPLUS DOES

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 

When 6 is variable, its influence on the solution in the neighborhood of a given 6 value is described by the matrix function 

The state trajectory u t) is computed by the implicit integrator DDASSL (Petzold 1982 Brenan, Campbell, and Petzold 1989). updated here to handle the initial condition of Eq. (B.1-2). The DDASSL integrator is especially designed to handle stiff, coupled systems of ordinary differential and algebraic equations. It employs a variable-order, variable-step predictor-corrector approach initiated by Gear (1971). The derivative vector applicable at t +i. is approximated in the corrector stage by a 

The sensitivity trajectory W t), when requested, is computed by the method of Caracotsios and Stewart (1985), extended here to include Eq. (B.l-4b). The sensitivities are computed at to and after each step, via a direct linear algorithm that utilizes the current matrix G of equation (B.l-5b) or (B.l-5a) to solve equation (B.l-4b) or a backward-difference form of (B.l-4a). 

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