In this paper a numerical approach for the optimization of stirrer configurations is presented. The methodology is based on a flow solver, and a mathematical optimization tool, which are integrated into an automated procedure. The flow solver is based on the discretization of the incompressible Navier-Stokes equations by means of a fully conservative finite-volume method for block-structured, b...

In this paper, we present some new variants of Chebyshev-Halley methods free from second derivative for solving nonlinear equation of the type f(x) = 0, and show that the convergence orders of the proposed methods are three or four. Several numerical examples are given to illustrate the efficiency and performance of the new methods.

Recently, the Runge-Kutta methods, obtained via Taylor’s expansion is exist in the literature. In this study, we have derived explicit methods for problems of the form y′ = f(y) including second and third derivatives , by considering available Two-Derivative Runge-Kutta methods (TDRK). The methods use one evaluation of first derivative, one evaluation of second derivative and many evaluations o...

In this study, derivative UV spectrophotometric methods were developed for the analysis of diflunisal, which is used as a nonsteroidal anti-inflammatory drug. Analysis wavelengths of diflunisal for the first and second order derivative UV spectrophotometric methods were obtained as 235.6 nm and 228.8 nm, respectively. The linearity ranges were found as 1.0-25.0 μg mL-1 for the first order and 1...

Derivative-free optimization focuses on designing methods to solve optimization problems without the analytical knowledge of the function. In this paper we consider the problem of designing derivative-free methods for finite minimax problems: minx maxi=1,2,...N{fi(x)}. In order to solve the problem efficiently, we seek to exploit the smooth substructure within the problem. Using ideas developed...

We consider the problem of minimizing a continuously differentiable function of several variables subject to simple bound constraints where some of the variables are restricted to take integer values. We assume that the first order derivatives of the objective function can be neither calculated nor approximated explicitly. This class of mixed integer nonlinear optimization problems arises frequ...

Variable-step (VS) second derivative $k$-step $3$-stage Hermite--Birkhoff--Obrechkoff (HBO) methods of order $p=(k+3)$, denoted by HBO$(p)$ are constructed as a combination of linear $k$-step methods of order $(p-2)$ and a second derivative two-step diagonally implicit $3$-stage Hermite--Birkhoff method of order 5 (DIHB5) for solving stiff ordinary differential equations. The main reason for co...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.