Analysis of a meshless method for the time fractional diffusion-wave equation

In this paper a numerical technique is proposed for solving the time fractional diffusion-wave equation. We obtain a time discrete scheme based on finite difference formula. Then, we prove that the time discrete scheme is unconditionally stable and convergent using the energy method and the convergence order of the time discrete scheme is \(\mathcal {O}(\tau ^{3-\alpha })\). Firstly, we change the main problem based on Dirichlet boundary condition to a new problem based on Robin boundary condition and then, we consider a semi-discrete scheme with Robin boundary condition and show when \(\beta \rightarrow +\infty \) solution of the main semi-discrete problem with Dirichlet boundary condition is convergent to the solution of the new semi-discrete problem with Robin boundary condition. We consider the new semi-discrete problem with Robin boundary condition and use the meshless Galerkin method to approximate the spatial derivatives. Finally, we obtain an error bound for the new problem. We prove that convergence order of the numerical scheme based on Galekin meshless is \(\mathcal {O}(h)\). In the considered method the appeared integrals are approximated using Gauss Legendre quadrature formula. The main aim of the current paper is to obtain an error estimate for the meshless Galerkin method based on the radial basis functions. Numerical examples confirm the efficiency and accuracy of the proposed scheme.     

Numerical solution of nonlinear Jaulent–Miodek and Whitham–Broer–Kaup equations

In this work we investigate the numerical solution of Jaulent–Miodek (JM) and Whitham–Broer–Kaup (WBK) equations. The proposed numerical schemes are based on the fourth-order time-stepping schemes in combination with discrete Fourier transform. We discretize the original partial differential equations (PDEs) with discrete Fourier transform in space and obtain a system of ordinary differential equations (ODEs) in Fourier space which will be solved with fourth order time-stepping methods. After transforming the equations to a system of ODEs, the linear operator in JM equation is diagonal but in WBK equation is not diagonal. However for WBK equation we can also implement the methods such as diagonal case which reduces the CPU time. Comparing numerical solutions with analytical solutions demonstrates that those methods are accurate and readily implemented.     

A new correlation based on artificial neural networks for predicting the natural gas compressibility factor

In this study a new correlation of natural gas compressibility factor based on theory of Mohammadikhah-Mohebbi-Abolghasemi??s equation of state (MMA EOS) is developed using an artificial neural network. In MMA EOS, the compressibility factor as a function of M-factor (BP/RT) is expressed. An artificial neural network (ANN) is designed in which the M-factor, reduced temperature, and reduced pressure are selected as input variables, whereas the natural gas compressibility factor is selected as output. Then, a new correlation based on the weights of ANN is obtained. Results of this correlation are compared with some other equations and experimental data. Proposed correlation for 597 data points has an average absolute deviation (AAD%) of 0.6% and a correlation coefficient (R ² value) of 0.9999.     

MHD forced convection of MWCNT–Fe3O4/water hybrid nanofluid in a partially heated τ-shaped channel using LBM

Journal of Thermal Analysis and Calorimetry - Forced convection heat transfer of multi-wall carbon nanotubes–iron oxide nanoparticles/water hybrid nanofluid (MWCNT–Fe3O4/water hybrid...     

Numerical investigation of MHD effects on nanofluid heat transfer in a baffled U-shaped enclosure using lattice Boltzmann method

Journal of Thermal Analysis and Calorimetry - Lattice Boltzmann method (LBM) was carried out to investigate the effects of magnetic field and nanofluid on the natural convection heat transfer in a...     

Development of green sodium sulfate‐induced solidification of floating organic droplets–dispersive liquid phase microextraction method: Application to extraction of four antidepressants

Sodium sulfate‐induced deep eutectic solvent–based solidification of floating organic droplets–dispersive liquid phase microextraction was developed prior to gas chromatography–mass spectrometry. In this method, a mixture of Na₂SO₄ solution (as phase separation agent and disperser) containing menthol–decanoic acid was rapidly injected into an alkaline aqueous solution containing Na₂SO₄. The solution was placed in an ice bath and the menthol–decanoic acid solvent was solidified on the surface of the solution. Under the optimal conditions, the enrichment factors and extraction recoveries were 122–147 and 74–89%, respectively. Finally, an aliquot of the collected organic phase was removed and mixed with acetonitrile and injected into the separation system. The limits of detection and lower limits of quantification were obtained at the ranges of 13–25 and 24–41 ng L^?1, respectively. The relative standard deviations of the proposed method were ≤11% for intra‐ and inter‐day precisions at four concentrations.     

Interaction of zanamivir with DNA and RNA: Models for drug–DNA and drug–RNA bindings

Zanamivir (ZAN) is the first of a new generation of influenza virus-specific drugs known as neuraminidase inhibitors, which acts by interfering with life cycles of influenza viruses A and B. It prevents the virus spreading infection to other cells by blocking the neuraminidase enzyme present on the surface of the virus. The aim of this study was to examine the stability and structural features of calf thymus DNA and yeast RNA complexes with zanamivir in aqueous solution, using constant DNA or RNA concentration (12.5 mM) and various zanamivir/polynucleotide (P) ratios of 1/20, 1/10, 1/4, and 1/2. FTIR and UV–visible spectroscopy are used to determine the drug external binding modes, the binding constant and the stability of zanamivir–DNA and RNA complexes in aqueous solution. Structural analysis showed major interaction of zanamivir with G-C (major groove) and A-T (minor groove) base pairs and minor perturbations of the backbone PO₂ group with overall binding constants of K_{zanamivir–DNA} = 1.30 × 10⁴ M⁻¹ and K_{zanamivir–RNA} = 1.38 × 10⁴ M⁻¹. The drug interaction induces a partial B to A-DNA transition, while RNA remains in A-conformation.     

High order compact solution of the one‐space‐dimensional linear hyperbolic equation

In this article, we introduce a high‐order accurate method for solving one‐space dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth order for discretizing spatial derivative of linear hyperbolic equation and collocation method for the time component. The main property of this method additional to its high‐order accuracy due to the fourth order discretization of spatial derivative, is its unconditionally stability. In this technique the solution is approximated by a polynomial at each grid point that its coefficients are determined by solving a linear system of equations. Numerical results show that the compact finite difference approximation of fourth order and collocation method produce a very efficient method for solving the one‐space‐dimensional linear hyperbolic equation. We compare the numerical results of this paper with numerical results of (Mohanty, 3 .© 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008     

Ultrasonic assisted headspace single drop micro-extraction and gas chromatography with nitrogen-phosphorus detector for determination of organophosphorus pesticides in soil

This work describes optimization of headspace single drop micro-extraction for extraction of five organophosphorus pesticides; thionazin, sulfotep, dimethoate, disulfoton and parathion in soil. Ultrasound has also been used successfully to improve and accelerate the extraction of the analytes from the sample. The optimized extraction performance was obtained when the experimental parameters were set as follows; 3.0 μL of octanol as extraction solvent, high ionic strength (20% sodium chloride), 1:1 (w/v) sample dilution with water, extraction temperature at 60 °C for 30 min; applying ultrasound and without any pH adjustment. The optimized method was linear over the calibration range (5–200 and 10–300 for different analytes) with limits of detection of 0.1–2.0 ng g⁻¹. The enrichment factor for OPPs was 1.4–12.7 and the method was also reproducible with the relative standard deviations (RSD%) of 2.1–6.9%.