For numerical solving of the present system, the unknown function F j ( t ) is approximated by its Bernstein approximation (3).
The presence of interfaces between regions with qualitatively and quantitatively different transport characteristics impose severe requirements to methods and numerical schemes used by solving of transport equations.
Kinetic modelling and FBA will reveal metabolite concentrations and metabolic fluxes, respectively, by numerical simulations solving the steady-state solutions of a metabolic network.
The level set method was presented by Osher and Sethian [20] who described the temporal propagation of moving interfaces by numerical methods solving the Hamilton Jacobi equation.
The developed mathematical model for a regeneration stage of 3A and 4A zeolites in TSA process was solved by numerical method of lines (NMOL).
Though the mechanism involved in these three stages are somewhat different, the whole breakout process can be simulated naturally using the present numerical model by solving a consolidation problem of the seabed subjected to various boundary conditions at the seabed surface below the disk.
In this response, the optimization process was repeated for the same numerical examples by directly solving coupled equations of motion.
Also, applicability of the method is demonstrated by solving numerical examples for different values of homogeneity variation parameter, aspect ratio, thickness to length ratio, foundation parameters, various types of boundary conditions and different numbers of point support.
Finally, we assess the accuracy of the plate model with respect to the parent three-dimensional model through two numerical benchmarks, solved by means of the finite element method.
The numerical results, obtained by solving a number of optimal control problems, are arranged into contour plots, characterized by different and well-defined behaviors depending on the value of the initial spacecraft propulsive acceleration, the final orbit radius, and the thruster's specific impulse.
