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. 相似文献
In this paper, a direct adaptive fuzzy controller with compensation signal is presented to control and stabilize a class of fractional order systems with unknown nonlinearities. Based on a Lyapunov function candidate the global Mittag–Leffler stability is proved and a new fractional order adaptation law is derived. The adaptation law adjusts free parameters of the fuzzy controller and bounds them by utilizing a novel fractional order projection algorithm. Furthermore, due to the use of compensation term, the proposed approach does not demand suitable membership functions in the fuzzy system. In addition, the stability of the closed-loop system is guaranteed by utilizing a supervisory controller. Numerical simulations show the validity and effectiveness of the introduced scheme for various fractional order nonlinear models that perturbed by disturbance and uncertainty. 相似文献
In this paper, we study the thermodynamics of quantum harmonic oscillator in the Tsallis framework and in the presence of a minimal length uncertainty. The existence of the minimal length is motivated by various theories such as string theory, loop quantum gravity, and black-hole physics. We analytically obtain the partition function, probability function, internal energy, and the specific heat capacity of the vibrational quantum system for \(1<q<\frac {3}{2}\) and compare the results with those of Tsallis and Boltzmann-Gibbs statistics without the minimal length scale. 相似文献
We propose a new initial condition for the homogeneous and isotropic quantum cosmology, where the source of the gravitational field is a conformally coupled scalar field, and the maximally symmetric hypersurfaces have positive curvature. After solving corresponding Wheeler–DeWitt equation, we obtain exact solutions in both classical and quantum levels. We propose appropriate initial condition for the wave packets which results in a complete classical and quantum correspondence. These wave packets closely follow the classical trajectories and peak on them. We also quantify this correspondence using de Broglie–Bohm interpretation of quantum mechanics. Using this proposal, the quantum potential vanishes along the Bohmian paths and the classical and Bohmian trajectories coincide with each other. We show that the model contains singularities even at the quantum level. Therefore, the resulting wave packets closely follow the classical trajectories from big-bang to big-crunch. 相似文献
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. 相似文献
We present a Chaplygin gas Friedmann-Robertson-Walker quantum cosmological model in the presence of the cosmological constant.
We apply the Schutz’s variational formalism to recover the notion of time, and this gives rise to Wheeler-DeWitt equation
for the scale factor. We study the early and late time universes and show that the presence of the Chaplygin gas leads to
an effective positive cosmological constant for the late times. This suggests the possibility of changing the sign of the
effective cosmological constant during the transition from the early times to the late times. For the case of an effective
negative cosmological constant for both epoches, we solve the resulting Wheeler-DeWitt equation using the Spectral Method
and find the eigenvalues and eigenfunctions for positive, zero, and negative constant spatial curvatures. Then, we use the
eigenfunctions in order to construct wave packets for each case and obtain the time-dependent expectation value of the scale
factors, which are found to oscillate between finite maximum and minimum values. Since the expectation value of the scale
factors never tend to the singular point, we have an initial indication that this model may not have singularities at the
quantum level. 相似文献
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. 相似文献
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.
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... 相似文献