A numerical method for solving linear integral equations of the second kind on the non-rectangular domains based on the meshless method

The main purpose of this article is to describe a numerical scheme for solving two-dimensional linear Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on radial basis functions (RBFs) constructed on a set of disordered data. The proposed method does not require any background mesh or cell structures, so it is meshless and consequently independent of the geometry of domain. This approach reduces the solution of the two-dimensional integral equation to the solution of a linear system of algebraic equations. The error analysis of the method is provided. The proposed scheme is also extended to linear mixed Volterra–Fredholm integral equations. Finally, some numerical examples are presented to illustrate the efficiency and accuracy of the new technique.     

Experimental study of the effect of disk obstacle rotating with Different angular ratios on heat transfer and pressure drop in a pipe with turbulent flow

Journal of Thermal Analysis and Calorimetry - This article presents the effects of a circular disk obstacle with different angle ratios on heat transfer and pressure drop under a turbulent flow...     

Thin plate spline Galerkin scheme for numerically solving nonlinear weakly singular Fredholm integral equations

The present work proposes a numerical method to obtain an approximate solution of non-linear weakly singular Fredholm integral equations. The discrete Galerkin method in addition to thin-plate splines established on scattered points is utilized to estimate the solution of these integral equations. The thin-plate splines can be regarded as a type of free shape parameter radial basis functions which create an efficient and stable technique to approximate a function. The discrete Galerkin method for the approximate solution of integral equations results from the numerical integration of all integrals in the method. We utilize a special accurate quadrature formula via the non-uniform composite Gauss-Legendre integration rule and employ it to compute the singular integrals appeared in the scheme. Since the approach does not need any background meshes, it can be identified as a meshless method. Error analysis is also given for the method. Illustrative examples are shown clearly the reliability and efficiency of the new scheme and confirm the theoretical error estimates.     

Simultaneous determination of ascorbic acid,dopamine, and uric acid using a carbon paste electrode modified with multiwalled carbon nanotubes,ionic liquid,and palladium nanoparticles

We describe the modification of a carbon paste electrode (CPE) with multiwalled carbon nanotubes (MWCNT) and an ionic liquid (IL). Electrochemical studies revealed an optimized composition of 60 % graphite, 20 % paraffin, 10 % MWCNT and 10 % IL. In a next step, the optimized CPE was modified with palladium nanoparticles (Pd-NPs) by applying a double-pulse electrochemical technique. The resulting electrode was characterized by scanning electron microscopy, energy dispersive X-ray spectroscopy, X-ray diffraction, cyclic voltammetry, and electrochemical impedance spectroscopy. It gives three sharp and well separated oxidation peaks for ascorbic acid (AA), dopamine (DA), and uric acid (UA), with peak separations of 180 and 200 mV for AA-DA and DA-UA, respectively. The sensor enables simultaneous determination of AA, DA and UA with linear responses from 0.6 to 112, 0.1 to 151, and 0.5 to 225 μM, respectively, and with 200, 30 and 150 nM detection limits (at an S/N of 3). The method was successfully applied to the determination of AA, DA, and UA in spiked samples of human serum and urine.

The CPE was modified with multiwalled carbon nanotubes and an ionic liquid. After optimization the electrode was further modified with palladium nanoparticles. The resulting electrode gives three sharp and well separated oxidation peaks for ascorbic acid, dopamine and uric acid

     

LOCAL GAUSSIAN-COLLOCATION SCHEME TO APPROXIMATE THE SOLUTION OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS USING VOLTERRA INTEGRAL EQUATIONS

This work describes an accurate and effective method for numerically solving a class of nonlinear fractional differential equations.To start the method,we equivalently convert these types of differential equations to nonlinear fractional Volterra integral equations of the second kind by integrating from both sides of them.Afterward,the solution of the mentioned Volterra integral equations can be estimated using the collocation method based on locally supported Gaussian functions.The local Gaussian-collocation scheme estimates the unknown function utilizing a small set of data instead of all points in the solution domain,so the proposed method uses much less computer memory and volume computing in comparison with global cases.We apply the composite non-uniform Gauss-Legendre quadrature formula to estimate singular-fractional integrals in the method.Because of the fact that the proposed scheme requires no cell structures on the domain,it is a meshless method.Furthermore,we obtain the error analysis of the proposed method and demon-strate that the convergence rate of the approach is arbitrarily high.Illustrative examples clearly show the reliability and efficiency of the new technique and confirm the theoretical error estimates.     

Experimental study on forced convection heat transfer of a nanofluid in a heat exchanger filled partially porous material

Journal of Thermal Analysis and Calorimetry - Heat transfer of MgO-EG nanofluid flowing in a double tube heat exchanger with an inner tube containing a partial porous material under laminar and...     

On local metric pressure of dynamical systems

In this paper, a local version of the topological pressure of dynamical systems is presented. It is a function defined on the product space which does not depend on any measure. It is shown that, for any invariant measure, integration of the introduced function with respect to its corresponding diagonal measure results in the metric pressure of the dynamical system.

     

Simultaneous determination of ascorbic acid,dopamine, and uric acid using a carbon paste electrode modified with multiwalled carbon nanotubes,ionic liquid,and palladium nanoparticles

We describe the modification of a carbon paste electrode (CPE) with multiwalled carbon nanotubes (MWCNT) and an ionic liquid (IL). Electrochemical studies revealed an optimized composition of 60 % graphite, 20 % paraffin, 10 % MWCNT and 10 % IL. In a next step, the optimized CPE was modified with palladium nanoparticles (Pd-NPs) by applying a double-pulse electrochemical technique. The resulting electrode was characterized by scanning electron microscopy, energy dispersive X-ray spectroscopy, X-ray diffraction, cyclic voltammetry, and electrochemical impedance spectroscopy. It gives three sharp and well separated oxidation peaks for ascorbic acid (AA), dopamine (DA), and uric acid (UA), with peak separations of 180 and 200 mV for AA-DA and DA-UA, respectively. The sensor enables simultaneous determination of AA, DA and UA with linear responses from 0.6 to 112, 0.1 to 151, and 0.5 to 225 μM, respectively, and with 200, 30 and 150 nM detection limits (at an S/N of 3). The method was successfully applied to the determination of AA, DA, and UA in spiked samples of human serum and urine. Figure

The CPE was modified with multiwalled carbon nanotubes and an ionic liquid. After optimization the electrode was further modified with palladium nanoparticles. The resulting electrode gives three sharp and well separated oxidation peaks for ascorbic acid, dopamine and uric acid     

A meshless method based on the moving least squares (MLS) approximation for the numerical solution of two-dimensional nonlinear integral equations of the second kind on non-rectangular domains

This paper investigates a numerical method for solving two-dimensional nonlinear Fredholm integral equations of the second kind on non-rectangular domains. The scheme utilizes the shape functions of the moving least squares (MLS) approximation constructed on scattered points as a basis in the discrete collocation method. The MLS methodology is an effective technique for approximating unknown functions which involves a locally weighted least square polynomial fitting. The proposed method is meshless, since it does not need any background mesh or cell structures and so it is independent of the geometry of the domain. The scheme reduces the solution of two-dimensional nonlinear integral equations to the solution of nonlinear systems of algebraic equations. The error analysis of the proposed method is provided. The efficiency and accuracy of the new technique are illustrated by several numerical examples.