On novel classes of iterative methods for solving nonlinear equations

In this paper, we establish two new classes of derivative-involved methods for solving single valued nonlinear equations of the form f(x) = 0. The first contributed two-step class includes two evaluations of the function and one of its first derivative where its error analysis shows a fourth-order convergence. Next, we construct a three-step high-order class of methods including four evaluations per full cycle to achieve the seventh-order of convergence. Numerical examples are included to re-verify the theoretical results and moreover put on show the efficiency of the new methods from our classes.     

Dispersive solid-phase extraction of risperidone from plasma samples using graphene oxide aerogels and determination with liquid chromatography

A graphene oxide-based aerogel was synthesized and applied to the extraction and the determinations with the high-performance liquid chromatography-ultraviolet detector. After the characterization of the produced graphene-aerogel, it was utilized as a dispersive solid-phase extraction sorbent for risperidone extraction from plasma samples. Aerogels are materials with a large surface area-to-mass ratio and plenty of core with functional groups which can easily attach to the analytes to extract them to the second phase. The suggested method determined risperidone in plasma samples in the wide dynamic range from 20 ng/ml to 3 μg/ml. The limits of detection and quantification of the developed method were calculated as 2.4 and 8.2 ng/ml, respectively. As a novel feature, the developed method has no need to precipitate plasma proteins, improving the analytical performance of the analysis. Also, for the first time, the produced materials were utilized for the extraction of risperidone from the plasma samples. The obtained results revealed that the developed approach could be employed as an accurate method for the quantification of risperidone in real plasma samples.