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Modeling, Optimization and Nonlinear Parameter Estimation for Scientists and Engineers


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DDAPLUS: Differential-Algebraic Solver and sensitivity analyzer for nonlinear initial-value problems in one dimension; also solves algebraic nonlinear equation systems. DDAPLUS is an extension of the solver DASSL (Petzold, 1982), considerably enhanced since the version of Caracotsios and Stewart, reference [2]. DDAPLUS provides superior initialization and no negativity control, stricter error control and reporting, optional optimization of the initial step size (even when the initial derivatives are zero), and the ability to stop and report at a target value of any designated variable. The basic algorithms are summarized in references [1], [2] and [3], listed on the following page.

GREGPLUS: A major enhancement of our nonlinear parameter estimation code GREG for process model analysis and sequential experimental design. Estimates the model parameters, their inference intervals and covariance, using single-response or multi-response data. Gives similar estimates for auxiliary functions of the parameters. Compares rival models, using replicate data along with objective criteria of posterior probability and goodness of fit. The code includes weighted nonlinear least squares, the multiresponse objective functions of Box and Draper [4] and Bard [5], and further developments from references [6], [7] and [8]. Diagnostics and corrective actions for over parameterized models are provided, including a display of the test divisors that determine which parameters are estimable according to the user's pivoting tolerance. Uninformative response variables are identified and set aside. Parametric sensitivities for the estimation can be coded by the user or can be generated accurately by GREG Plusís new adaptive finite-difference algorithms.   

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