In this paper, on the basis of information theory measures (statistical complexity and normalized Shannon entropy), the dynamical complexity of FitzHugh–Nagumo (FHN) neuron model under the co-excitation of Lévy noise and Gaussian white noise is studied. Because the potential function of the neuron system is asymmetric, we consider not only the total residence time interval of the system, but also the

In this study, a new evolutionary optimized finite difference based computing paradigm is presented for dynamical analysis of dust density model for the ensemble of electrical charges and dust particles represented with nonlinear oscillatory system based on hybridization of Van-der Pol and Mathieu equation (VDP-ME). Strength of accurate and effective discretization ability of finite difference method

To describe the dynamical ordering behaviour of a risk-averse newsvendor with trade credit in supply chain, two models are formulated for two scenarios based on the bounded rationality rule. Assuming the newsvendor chooses the ordering quantity by adaptively adjusting the choice of previous period, we first develop a deterministic model. Then, mathematical analysis of the model is provided, such as

Here we deliberate a new class of nano-materials with two different types of nanoparticles which immensely magnify the thermo-physical properties and thermal transport proficiency of nano-liquid. Prandtl number exhibits a primitive role in regulating thermal or momentum boundary layer regions. Therefore, keeping such comprehensive spectrum in view we contemplated MHD natural convection flow of steady

To estimate travel time through a composite ring road, a viscoelastic traffic flow model is developed by assuming traffic sound speed on empty road is just equal to free flow speed. Based on the viscoelastic model, numerical tests of traffic flows were conducted to provide node traffic speed for estimating travel time. The composite ring road with three ramp intersections has five parts, each part

This paper considers an impulsive switching human immunodeficiency virus (HIV) infection model incorporating the mean-reverting Ornstein–Uhlenbeck process. The model involve the virus-to-cell infection and cell-to-cell transmission and has an explicit age-dependent structure. Due to the exact solution of this system can not be expressed explicitly, it is necessary to give a suitable numerical method

In the current paper, for the time fractional diffusion equation with an exponential tempering, we propose a numerical algorithm based on the Lagrange-quadratic spline interpolations and the optimal technique. The discretized linear systems and some properties are investigated in details. By using these properties, the coefficient matrix and the right-hand term at each time step are given to analyze

Natural convection (NC) in high permeable porous media is usually investigated using the Darcy-Lapwood-Brinkman model (DLB). The problem of the porous squared cavity is widely used as a common benchmark case for NC in porous media. The solutions to this problem with the DLB model are limited to steady-state conditions. In this paper, we developed a time-dependent high accurate solution based on the

We propose a new approach for meshless multi-level radial basis function (ML-RBF) approximation which offers data-sensitive compression and progressive details visualization. It leads to an analytical description of compressed vector fields, too. The proposed approach approximates the vector field at multiple levels of detail. The low-level approximation removes minor flow patterns while the global

In this paper, the problem of bifurcation for a fractional order predator–prey system involving two nonidentical delays is discussed. The critical values of delays for Hopf bifurcation are exactly figured out for the proposed model by using two nonidentical delays as bifurcation parameter, respectively. In addition, the effects of fractional order and additional delay on the bifurcation point are carefully

We consider the application of the Kansa–radial basis function (RBF) collocation method to two–dimensional fourth order boundary value problems (BVPs). The presence of two boundary conditions makes it necessary to use a second set of centres corresponding to the second boundary condition. One option is to take these centres on the boundary but at different positions to the original boundary centres

This paper is concerned with numerical methods for a class of nonhomogeneous Neumann problems of time-fractional reaction–diffusion equations with variable coefficients. The solutions of this kind of problems often have weak singularity at the initial time. This makes the existing numerical methods with uniform time mesh often lose accuracy. In this paper, we propose and analyze a high-order compact

In this paper, we study the numerical solution of the Riesz space fractional Sine-Gordon equations. We develop an explicit fourth-order energy-preserving difference scheme for the two-dimensional space fractional Sine-Gordon equation (SGE). The conservation, convergence and boundedness properties of the numerical scheme are rigorously proved. Subsequently, the proposed numerical method is applied to

Images are often corrupted by noise during their process of acquisition, storage and transmission. This alteration usually deteriorates the perception quality of the image. The central challenge in image denoising corresponds to eliminating the corrupted information while it is maintained the fine features of the original image. Anisotropic Diffusion (AD) is considered a well-established scheme for

In this paper, wave propagation in a two-layer composite strip is investigated analytically and numerically. The strip is loaded by a very short transverse stress pulse. Three cases of the strip problem are assumed: (i) isotropic aluminum Al strip and two-layer strips made of (ii) Al and the ceramics Al2O3 and (iii) the ceramics Al2O3 and Al. The analytical method is based on Laplace and Fourier transform

Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy-tailed distributions and distributions with analytically intractable densities turns out to be rather problematic. In this paper, we propose a novel approach towards the use of

In this article we propose fully discrete least-squares spectral element method for parabolic interface problems in R2. Crank–Nicolson scheme is used in time and higher order spectral elements are used in the spatial direction. This method is based on the nonconforming spectral element method proposed in Kishore Kumar and Naga Raju (2012). The proposed method is least-squares spectral element method

The salp swarm algorithm (SSA) is a recent and straightforward swarm intelligent optimizer. It mainly simulates the foraging and navigational behavior of salp in the ocean by forming a salp chain. The salp in the front of the chain guides the moving direction of the population, which makes the algorithm easy to fall into local optimum and lead to premature convergence. In order to tackle this shortcoming

This paper addresses the problem of event-triggered dynamic output feedback control for uncertain Markovian jump systems with partly unknown transition rates. An event-triggered dynamic output feedback control scheme is proposed to stabilize a class of uncertain networked Markovian jump systems with partly unknown transition rates, and a suitable Lyapunov-Krasovski functional is then introduced to

The idea of the current investigation is to analyze the effect of thermal radiation and non-uniform heat source/sink on unsteady MHD micropolar fluid flow past a stretching/shirking sheet. The governing non-linear PDEs are transformed into a set of non-linear coupled ODEs which are then solved numerically by using the fourth order predictor–corrector finite difference method (PC4-FDM). The effect of

This paper investigates a stochastic Markovian switching predator–prey model with infinite memory and general Lévy jumps. Firstly, we transfer a classic infinite memory predator–prey model with weak kernel case into an equivalent model through integral transform. Then, for the corresponding stochastic Markovian switching model, we establish the sufficient conditions for permanence in time average and

The present work attempts to show the accuracy of lattice Boltzmann method (LBM) to study a liquid flow with volumetric forces of electroosmotic and pressure gradient over hydrophobic surfaces. Navier boundary condition, slip velocity and temperature jump are taken into account. The flow has temperature-dependent physical properties and is assumed to be laminar, steady and viscous. Joule heating effects

In this paper, we investigate the fractional Biswas–Milovic model having Kerr and parabolic law nonlinearities via the application of fractional complex transform (FCT) coupled with the homotopy perturbation transform technique (HPTT). HPTT is a fusion of homotopy perturbation method with Laplace transform The obtained numerical results are demonstrated through graphs and tables. The numerical simulation

The water wave optimization (WWO) algorithm is inspired by shallow water wave theory and mainly simulates propagation, refraction and breaking to obtain the global optimal solution in the search space. Due to its premature convergence and low optimization efficiency, the basic WWO has a slow convergence speed and low calculation accuracy. To improve the overall optimization performance of the basic

In this paper, we study the centralized fusion (CF) and weighted measurement fusion (WMF) robust steady-state Kalman filtering problem for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, two-step random delays, missing measurements, and uncertain noise variances. By using a model transformation approach consisting of augmented approach, de-randomization

A new solver, via the enthalpy multiple-relaxation lattice Boltzmann method, is developed to simulate the Ga melting (considering Ga as a phase change material) for different settings. At first, the phase change simulation of a simple bar is performed, this case is implemented to validate the heat transfer in our model via the analytical solution. Second, the solid–liquid phase change simulation with

The problem of passivity-based sliding mode control is considered, for the unified chaotic system having uncertainties and perturbations. Using a combination between sliding mode method and the passivity method, an appropriate switching surface for the uncertain and perturbed system is designed, and then through passivity theory, the stability of the system is ensured. The proposed design is applied

Uncertain heat equation (for short, UHE) is a type of second-order uncertain PDEs driven by Liu processes. In most cases, since it is tough to get the analytic solution for a UHE, we must find a way to obtain its numerical solution. A forward difference scheme has been designed to solve UHE, but our paper will show that this method may exhibit instability in some situations. We explore another approach

In this comment, we show that the exact solution of the RKL model which has been obtained by Triki and Taha (2009) is not true. Then, the exact analytic solutions of the RKL model are derived with constraint conditions.

In this paper, we consider a fast algorithm to calculate a two-dimensional nonlinear time distributed-order and space fractional diffusion equation, which is called the time two-mesh (TT-M) finite element (FE) method. In time, the TT-M algorithm combined with both the implicit second-order σ backward difference formula and Crank–Nicolson scheme for computing the numerical solution at time t1 is used

The dynamics of COVID-19 is investigated with regard to complex contributions of the omitted factors. For this purpose, we use a fractional order SEIR model which allows us to calculate the number of infections considering the chaotic contributions into susceptible, exposed, infectious and removed number of individuals. We check our model on Wuhan, China-2019 and South Korea underlying the importance

Simultaneous effects of non-Newtonian and curvature on unsteady nano-fluid flow through overlapping stenosed channel have been investigated in this letter. In this numerical investigation, a mathematical formulation is developed in order to analyze the influence of blood shear thinning/thickening effects on the rheology of the nano-fluid within curved channel which is not explored yet. Moreover, the

The purpose of this paper is to prove a priori error estimates for the completely discretized problem of the dual mixed method for the non-stationary heat diffusion equation in a polygonal domain of R2. Due to the geometric singularities of the domain, the exact solution is not regular in the context of classical Sobolev spaces. Instead, one must use weighted Sobolev spaces in our analysis. To obtain

In this paper, we classify the fixed and critical points of the bi-parametric family of Ostrowski–Chun methods applied on quadratic polynomials. We obtain the values of the parameters that reduce the number of free critical points. We select the one-parametric subfamilies with only one free critical point and we carry out a dynamical study of these subfamilies. For each subfamily we study the parameter

A new finite difference collocation algorithm has been introduced with the help of Fibonacci polynomial and then applied to one super and two sub-diffusion problems having an exact solution. It has also been shown that numerical error obtained with the investigated method is more accurate than previously existing methods. Fractional order reaction advection sub-diffusion equation containing Caputo

We provide a uniformly efficient and simple random variate generator for the truncated negative gamma distribution restricted to any interval.

In this paper, we introduce a regime-switching model, such that the volatility of the model depends on the asset price. In this model, the interest rate and the volatility are associated with regime changes. Since the market model has the arbitrage opportunity, we derive an equivalent martingale measure for pricing an arithmetic Asian option. To evaluate the price of an arithmetic Asian option, we

The objective of the work in this paper is to computationally tackle a range of problems in hyperbolic conservation laws, which is an interesting branch of computational fluid dynamics. For the simulation of issues in hyperbolic conservation laws, this work explores the concept of fuzzy logic-based operators. This research presents a unique mixture of fuzzy sets and logic with a new branch of conservation

We study a fictitious domain decomposition method for a nonlinearly bonded structure. Starting with a strongly convex unconstrained minimization problem, we introduce an interface unknown such that the displacement problems on each subdomain become uncoupled in the saddle-point equations. The interface unknown is eliminated and a Uzawa conjugate gradient domain decomposition method is derived from

The estimation of a finite population distribution function is considered when there are missing data. Calibration adjustment is used for dealing with nonresponse at the estimation stage. Several procedures are proposed and compared. A numerical study is carried out to evaluate the performances of estimators. Computational problems with the implementation of the proposed calibration estimators are

Many local integral methods are based on an integral formulation over small and heavily overlapping stencils with local Radial Basis Functions (RBFs) interpolations. These functions have become an extremely effective tool for interpolation on scattered node sets, however the ill-conditioning of the interpolation matrix – when the RBF shape parameter tends to zero corresponding to best accuracy – is

Based on fractional generalized Adams methods, a numerical method is constructed for solving fractional delay differential equations. The convergence of the method is analyzed in detail. The stability of the fractional generalized Adams methods for fractional ordinary differential equations is generalized to a general framework. Under such framework, the linear stability of the method is studied for

A mathematical model for the CD8+ T-cell response to Human T cell leukemia/lymphoma virus type I (HTLV-I) infection is investigated in this paper. The proposed model, which involves four coupled nonlinear ordinary differential equations, describes the interaction of uninfected CD4+T cells, latently infected CD4+T cells, actively infected CD4+T cells and HTLV-I specific cytotoxic T-lymphocytes (CTLs)

A comparative assessment between SIMPLE and its variant SIMPLE-C is conducted based on two-dimensional (2-D) incompressible flows, using a cell-centered finite-volume Δ-formulation on a collocated grid. The SIMPLE-C (SIMPLE Compressibility) scheme additionally combines the concept of artificial compressibility (AC) with the pressure Poisson equation, provoking the diagonal dominance of influence coefficients

The objective of this study is to analyze the numerical intervals of the Human Immunodeficiency Virus (HIV) using the solution of a dynamics model at each time iteration, considering the infection rate of CD4+ T lymphocytes and the production rate of the virus as outputs of an interval type-2 Fuzzy Rule-Based System (FRBS). The mathematical model consists of a system of ordinary differential equations

In this paper, multiple-order line rogue waves of extended Kadomtsev–Petviashvili equation are constructed based on the Hirota bilinear method and symbolic computation approach. Motion trajectories and minimum and maximum values of the first-order line rogue wave solutions are analyzed in detail. Furthermore, both second-order and third-order line rogue waves are explicitly derived and their complex

Heat radiation in optically thick non-grey media can be well approximated with the Rosseland model which is a class of nonlinear diffusion equations with convective boundary conditions. The optical spectrum is divided into a set of finite bands with constant absorption coefficients but with variable Planckian diffusion coefficients. This simplification reduces the computational costs significantly

In this paper, we propose a two-level difference scheme for solving the two-dimensional Fokker–Planck equation. This equation is a parabolic type equation which governs the time evolution of probability density function of the stochastic processes. In addition, these equations preserve positivity and conservation. The Chang–Cooper discretization scheme is used, which ensures second-order accuracy,

Predictor–corrector schemes are designed to be a compromise to retain the stability properties of the implicit schemes and the computational efficiency of the explicit ones. In this paper a complete analytical study for the linear mean-square stability of the two-parameter family of Euler predictor–corrector schemes for scalar stochastic differential equations is given. The analyzed family is given

The commuters’ circulation space in the multimodal transport interchanges comprises of a network of pathways and stairways and meant for the efficient transit of commuters from one mode to another transport mode. Transit Cooperative Research Program (TCRP) - Report 165 guidelines for the design of commuters’ circulation space in multimodal transport interchanges has several shortcomings. To aid the

In this paper, we present a framework for achieving circular formation of a two-dimensional moving target using a team of underactuated Omni-Directional Intelligent Navigator (ODIN) vehicles. The main goal is to ensure uniform circumnavigation of the moving target with prescribed radius, velocity and inter-vehicle spacing. In the formation, part of vehicle group is capable of obtaining information

A method is presented for the numerical solution of odd-order nonlinear boundary value problems with complementary Lidstone boundary conditions. The approximate solution is given in terms of spline interpolation functions, written in the Lidstone second type polynomial basis. Some results on local and global errors are given. Numerical tests are presented.

In this paper, we develop a machine learning method with the Least Squares Support Vector Regression (LS-SVR) for the numerical solution of Fredholm integral equations. Two different approaches are proposed for training the network by using the shifted Legendre kernel, the collocation and Galerkin LS-SVR approaches. As with the standard LS-SVR for known dataset regression, the formulation of the method

We propose an enhanced multi-objective harmony search (EMOHS) algorithm and a Gaussian mutation to solve the flexible flow shop scheduling problems with sequence-based setup time, transportation time, and probable rework. A constructive heuristic is used to generate the initial solution, and clustering is applied to improve the solution. The proposed algorithm uses response surface methodology to minimize

Cell migration is fundamental in a wide variety of physiological and pathological phenomena, being exploited in biomedical engineering as well. In this respect, we here present a hybrid non-local integro-differential model where a representative cell, reproduced by a point particle with an orientation, moves on a planar domain upon signals coming from environmental variables. From a numerical point

This paper proposes and studies a novel test for the geometric distribution which is based on a characterization of that law in terms of the conditional expectation of the second order statistic, given the value of the first order statistic. The asymptotic null distribution of the test statistic and its limit under general conditions are derived, proving that it is consistent against fixed alternatives

In the light of the potential applications in engineering, electronics, physics, chemistry, and biology, the current work applies several techniques to achieve analytic approximate and numerical solutions of the cubic–quintic Duffing–van der Pol equation. This equation represents a second-order ordinary differential equation with quintic nonlinearity and includes two external periodic forcing terms

In this paper, the implicit assumptions in Levesque’s approximation are re-examined, and the dimensionless temperature distribution and the thermal boundary layer thickness were illustrated using the developed solution. By defining a similarity variable, the governing equations and boundary conditions are reduced to a typical dimensionless form in order to achieve an analytic solution in the entrance

In this paper, an efficient finite difference scheme is developed for solving the time-fractional Cahn–Hilliard equations which is the well-known representative of phase-field models. The time Caputo derivative is approximated by the popular L1 formula. The stability and convergence of the finite difference scheme in the discrete L2-norm are proved by the discrete energy method. To compare and observe

In this paper, we introduce two different methods based on Gegenbauer wavelet and Bernoulli wavelet for the solution of neutral delay differential equations. These methods convert linear and nonlinear neutral delay differential equations into system of linear and nonlinear algebraic equations, respectively. After solving these equations, we get the approximate solutions. Here, we have used the Gegenbauer