Numerical solution of the controlled Duffing oscillator by hybrid functions

A numerical method for solving the controlled Duffing oscillator is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions which consists of block-pulse functions plus Legendre polynomials are given. The method is based upon expanding various time functions in the system as their truncated hybrid functions. The operational matrix of product is introduced. This matrix together with the operational matrix of integration are utilized to reduce the solution of controlled Duffing oscillator to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.     

The effect of rib shape on the behavior of laminar flow of oil/MWCNT nanofluid in a rectangular microchannel

Journal of Thermal Analysis and Calorimetry - In this research, the laminar and forced flow and heat transfer of oil/multi-walled carbon nanotubes nanofluid in a microchannel have been numerically...     

Solution of Volterra's population model via block‐pulse functions and Lagrange‐interpolating polynomials

A numerical method for solving Volterra's population model for population growth of a species in a closed system is proposed. Volterra's model is a nonlinear integro‐differential equation where the integral term represents the effects of toxin. The approach is based on hybrid function approximations. The properties of hybrid functions that consist of block‐pulse and Lagrange‐interpolating polynomials are presented. The associated operational matrices of integration and product are then utilized to reduce the solution of Volterra's model to the solution of a system of algebraic equations. The method is easy to implement and computationally very attractive. Applications are demonstrated through an illustrative example. Copyright © 2008 John Wiley & Sons, Ltd.     

Determination of 11 priority pollutant phenols in wastewater using dispersive liquid—liquid microextraction followed by high-performance liquid chromatography—diode-array detection

Dispersive liquid—liquid microextraction coupled with high-performance liquid chromatography—diode-array detection was applied for the extraction and determination of 11 priority pollutant phenols in wastewater samples. The analytes were extracted from a 5-mL sample solution using a mixture of carbon disulfide as the extraction solvent and acetone as the dispersive solvent. After extraction, solvent exchange was carried out by evaporating the solvent and then reconstituting the residue in a mixture of methanol–water (30:70). The influences of different experimental dispersive liquid—liquid microextraction parameters such as extraction solvent type, dispersive solvent type, extraction and dispersive solvent volume, salt addition, and pH were studied. Under optimal conditions, namely pH 2, 165-μL extraction solvent volume, 2.50-mL dispersive solvent volume, and no salt addition, enrichment factors and limits of detection ranged over 30–373 and 0.01–1.3 μg/L, respectively. The relative standard deviation for spiked wastewater samples at 10 μg/L of each phenol ranged between 4.3 and 19.3% (n = 5). The relative recovery for wastewater samples at a spiked level of 10 μg/L varied from 65.5 to 108.3%.     

Analysis of time-varying delay systems via triangular functions

This paper presents a method for finding the analysis of time-varying delay systems using triangular functions. We present the properties of the triangular functions. The operational matrices of integration, delay and product are utilized to reduce the solution of delay systems to the solution of algebraic equations. Illustrative examples is included to demonstrate the validity and applicability of the technique.     

Hybrid functions for nonlinear initial-value problems with applications to Lane-Emden type equations

A numerical method for solving nonlinear initial-value problems is proposed. The Lane-Emden type equations which have many applications in mathematical physics are then considered. The method is based upon hybrid function approximations. The properties of hybrid of block-pulse functions and Lagrange interpolating polynomials are presented and are utilized to reduce the computation of nonlinear initial-value problems to a system of non-algebraic equations. The method is easy to implement and yields very accurate results.     

A hybrid approximation method for solving Hutchinson’s equation

The hybrid function approximation method for solving Hutchinson’s equation which is a nonlinear delay partial differential equation, is investigated. The properties of hybrid of block-pulse functions and Lagrange interpolating polynomials based on Legendre-Gauss-type points are presented and are utilized to replace the system of nonlinear delay differential equations resulting from the application of Legendre pseudospectral method, by a system of nonlinear algebraic equations. The validity and applicability of the proposed method are demonstrated through two illustrative examples on Hutchinson’s equation.     

Transition-metal-free oxidative amidation of benzyl alcohols with amines catalyzed by NaI: a new method for the synthesis of benzamides

A simple, inexpensive, and efficient method for the synthesis of benzamides via the reaction of benzyl alcohols and amine hydrochloride salts in the presence of NaI as a green catalyst is described. Various derivatives of benzamide were synthesized in moderate to good yields using this method.