Numerical Treatment of DAE and Applications
Two major problems in the solution of DAEs are index reduction and consistent initial conditions. Most numerical solvers require ordinary differential equations and algebraic equations of the form
It is a non-trivial task to convert arbitrary DAE systems into ODEs for solution by pure ODE solvers. Techniques which can be employed include Pantelides algorithm and dummy variable substitution. Alternatively, a direct solution of high index DAEs with inconsistent initial conditions is also possible. This solution approach involves a transformation of the derivative elements through orthogonal collocation on finite elements or direct transcription into algebraic expressions. This allows DAEs of any index to be solved without rearrangement in the open equation form
Once the model has been converted to algebraic equation form, it is solvable by large-scale nonlinear programming solvers (see APMonitor).
Read more about this topic: Differential Algebraic Equation
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