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Implementation Guidelines for ODE Models

If the dimensionality of the problem is not excessively high, simultaneous integration of the state and sensitivity equations is the easiest approach to implement the Gauss-Newton method without the need to store x(t) as a function of time. The latter is required in the evaluation of the Jacobeans in Equation 6.9 during the solution of this differential equation to obtain G(t). [Pg.88]

In this case the n-dimemional vector gi represents the sensitivity coefficients of the state variables with respect to parameter k, and satisfies the following ODE, [Pg.88]

Finally for the last parameter, kp, we have the corresponding sensitivity vector gp [Pg.89]

Since most of the numerical differential equation solvers require the equations to be integrated to be of the form [Pg.89]


Implementation Guidelines for ODE Models The Gauss-Newton Method — Nonlinear Output Relationship The Gauss-Newton Method - Systems with Unknown Initial Conditions Examples... [Pg.15]

Selection of Weighting Matrix Q in Least Squares Estimation Implementation Guidelines for ODE Models... [Pg.16]

This indicates that after an initial overhead of 0.319 model runs to set up the algorithm, an additional 0.07 of a model-run was required for the computation of the sensitivity coefficients for each additional parameter. This is about 14 times less compared to the one additional model-run required by the standard implementation of the Gauss-Newton method. Obviously these numbers serve only as a guideline however, the computational savings realized through the efficient integration of the sensitivity ODEs are expected to be very significant whenever an implicit or semi-implicit reservoir simulator is involved. [Pg.375]


See other pages where Implementation Guidelines for ODE Models is mentioned: [Pg.88]    [Pg.148]    [Pg.109]    [Pg.169]    [Pg.88]    [Pg.148]    [Pg.109]    [Pg.169]   


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