In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

‎In this paper a new family of fifteenth-order methods with high efficiency index is presented‎. This family include four evaluations of the function and one evaluation of its first derivative per iteration.‎ ‎Therefore‎, ‎this family of methods has the efficiency index which equals 1.71877‎. ‎In order to show the applicability and validity of the class‎, ‎some numerical examples are discussed‎.

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.    

Three simple and rapid spectrophotometric methods were developed for detection and trace determination of benzophenone (the main impurity) in phenytoin bulk powder and pharmaceutical formulations. The first method, zero-crossing first derivative spectrophotometry, depends on measuring the first derivative trough values at 257.6 nm for benzophenone. The second method, zero-crossing third derivat...

In some optimization problems found in applications, the derivatives of the objective function can be computed or approximated but at an expensive cost, and it is desirable to know when to use derivative-free methods (such as direct search, for instance) or derivativebased methods (such as gradient or quasi-Newton methods). Derivative-free methods may achieve a steady initial progress for some ...

This paper is a review of the authors’ results on the Dynamical Systems Method (DSM) for solving operator equation (*) F (u)= f . It is assumed that (*) is solvable. The novel feature of the results is the minimal assumption on the smoothness of F . It is assumed that F is continuously Fréchet differentiable, but no smoothness assumptions on F ′(u) are imposed. The DSM for solving equation (*) ...

Zero, first and second order derivative spectrophotometric methods were developed for the determination of insulin. The standard solutions and pharmaceutical sample were prepared in 0.01 M HCl. Absorbences of insulin were measured at 276 nm for the zero order by measuring height of peak from zero, at 264, 277 and 284 nm for the first order and at 277, 280, 283 and 289 nm for second order deriva...