Pub. online:1 Jan 2018Type:Research ArticleOpen Access
Volume 29, Issue 2 (2018), pp. 233–249
The new nonlocal delayed feedback controller is used to control the production of drugs in a simple bioreactor. This bioreactor is based on the enzymatic conversion of substrate into the required product. The dynamics of this device is described by a system of two nonstationary nonlinear diffusion-reaction equations. The control loop defines the changes of the substrate concentration delivered into the bioreactor at the external boundary of the bioreactor depending on the difference of measurements of the produced drug delivered into the body and the flux of the drug prescribed by a doctor in accordance with the therapeutic protocol. The system of PDEs is solved by using the finite difference method, the control loop parameters are defined from the analysis of stationary linearized equations. The stability of the algorithm for the inverse boundary condition is investigated. Results of computational experiments are presented and analysed.
Pub. online:1 Jan 2000Type:Research ArticleOpen Access
Volume 11, Issue 4 (2000), pp. 371–380
The accuracy of adaptive integration algorithms for solving stiff ODE is investigated. The analysis is done by comparing the discrete and exact amplification factors of the equations. It is proved that the usage of stiffness number of the Jacobian matrix is sufficient in order to estimate the complexity of solving ODE problems by explicit integration algorithms. The complexity of implicit integration algorithms depends on the distribution of eigenvalues of the Jacobian. Results of numerical experiments are presented.