This means: the desired optimal stochastic solution can be calculated from the solution to the deterministic problem, by replacing the state variable with their optimal estimates, which can be generated online following a Kalman filter scheme.
The gradient of the objective function is easily calculated from the solution of the system.
Average ion activity products calculated from the solution chemistry at 95 and 115°C are listed in Table 9.
The coefficients, obtained by Galerkin type of error minimisation, can be calculated from the solution of an extended set of linear algebraic equations.
Hence, the state feedback sampled-data control gains are calculated from the solution of a new and specific two-point boundary value problem.
In the implementation of spectral difference (SD) method, the conserved variables at the flux points are calculated from the solution points using extrapolation or interpolation schemes.
The wave propagation is modeled by a finite-element approximation of the Helmholtz equation, and the necessary objective-function gradient is calculated from the solution of the associated adjoint equation.
Theoretical breakthrough curves for saturation and regeneration of a molecular sieve adsorption column are calculated from the solution of the appropriate diffusion equation for the case of micropore diffusion control.
The optimization scheme minimizes the discrepancy ∥θm x,t)−θ x,t qo)∥L2 ΓI×[0,tmax]) between the temperature θ x,t qo) calculated from the solution of a direct problem for each flux qo and the desired (or measured) temperature θm x,t) on the boundary ΓI.
