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APMonitor
Advanced process monitor (APMonitor), is a modeling language for differential algebraic (DAE) equations. It is a free web-service for solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of linear programming, integer programming, nonlinear programming, nonlinear mixed integer programming, dynamic simulation, moving horizon estimation, and nonlinear control. APMonitor does not solve the problems directly, but calls nonlinear programming solvers such as APOPT, BPOPT, IPOPT, MINOS, and SNOPT. The APMonitor API provides exact first and second derivatives of continuous functions to the solvers through automatic differentiation and in sparse matrix form.
==High Index DAEs==
The highest order of a derivative that is necessary to return a DAE to ODE form is called the ''differentiation index''. A standard way for dealing with high-index DAEs is to differentiate the equations to put them in index-1 DAE or ODE form (see Pantelides algorithm). However, this approach can cause a number of undesirable numerical issues such as instability. While the syntax is similar to other modeling languages such as gProms, APMonitor solves DAEs of any index without rearrangement or differentiation. As an example, an index-3 DAE is shown below for the pendulum motion equations and lower index rearrangements can return this system of equations to ODE form (see (Index 0 to 3 Pendulum example )).
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