Compound and Other Optimum Designs for Systems of Nonlinear Differential Equations Arising in Chemical Kinetics
نویسنده
چکیده
The optimum design of experiments for nonlinear models requires parameter sensitivities, that is the derivatives of the response with respect to the parameters. If the differential equations forming the kinetic model do not have an analytical solution, numerical derivatives have to be used. We describe the “direct” method for calculating the sensitivities and apply it to the design of experiments for estimating the order of chemical reactions.
منابع مشابه
Differential transform method for a a nonlinear system of differential equations arising in HIV infection of CD4+T cell
In this paper, differential transform method (DTM) is described and is applied to solve systems of nonlinear ordinary differential equations which is arising in HIV infections of cell. Intervals of validity of the solution will be extended by using Pade approximation. The results also will be compared with those results obtained by Runge-Kutta method. The technique is described and is illustrat...
متن کاملConstuction of solitary solutions for nonlinear differential-difference equations via Adomain decomposition method
Here, Adomian decomposition method has been used for finding approximateand numerical solutions of nonlinear differential difference equations arising inmathematical physics. Two models of special interest in physics, namely, theHybrid nonlinear differential difference equation and Relativistic Toda couplednonlinear differential-difference equation are chosen to illustrate the validity andthe g...
متن کاملApproximate solution of system of nonlinear Volterra integro-differential equations by using Bernstein collocation method
This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the giv...
متن کاملSolving nonlinear space-time fractional differential equations via ansatz method
In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...
متن کاملChebyshev finite difference method for solving a mathematical model arising in wastewater treatment plants
The Chebyshev finite difference method is applied to solve a system of two coupled nonlinear Lane-Emden differential equations arising in mathematical modelling of the excess sludge production from wastewater treatment plants. This method is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The approach consists of reducing the ...
متن کامل