As a popular sampling tool used for Monte Carlo computing, importance sampling (IS) has been used in a wide variety of application areas recently. In large-scale survey data such as Chinese General Social Survey (CGSS), missing data, a high level of skewness and heteroscedastic variances commonly occur. Most of the existing literatures on survey data analysis focused on modeling the conditional mean

Firstly, a dynamic analysis for reaction–diffusion Gilpin–Ayala competition model involved in harmful species is considered under Dirichlet boundary value condition. Existence of multiple stationary solutions is verified by way of Mountain Pass lemma, and the local stability result of the null solution is obtained by employing linear approximation principle. Secondly, the authors utilize variational

This study investigated the impact of white noise on the HIV/AIDS model with a cytotoxic T lymphocyte (CTL) immune response. The model introduced the interactions between the virus and two kinds of target cells, CD4+ T cells and macrophages. It was theoretically proved that the solution of the stochastic model is positive and global, as well as the existence of an ergodic stationary distribution. The

Predicting electricity consumption is not an easy task depending on many factors that affect energy consumption. Therefore, electricity utilities and governments are always searching for intelligent models to improve the accuracy of prediction and recently, deep learning becomes the most used field in prediction. In this paper, we introduce a deep learning model based on deep feedforward neural networks

In this work we propose a simple and efficient algorithm to numerically approximate the time-dependent implied volatility for jump-diffusion models in option pricing that generalize the Black–Scholes equation. Here we use implicit-explicit difference schemes to compute the derivative part with fully implicit method and the integral term – in an explicit way. An average in time linearization of the

In this work, a study of the mathematical model of uncontrolled growth of tumor cells in the presence of chemotherapy is proposed. The fractional form of the model with the non-singular exponential kernel is considered. This model consists of four coupled partial differential equations (PDEs) which depict the relationship among the normal, tumor, immune cells, and the chemotherapy parameter. The purpose

In this work, we describe a simulation framework for fluid movement in a corrugated sawtooth channel whose walls are undergoing periodic repeated oscillations. The sawtooth geometry of the channel walls creates a fluid ratchet by generating an anisotropy in the fluid impedance. The simulations are developed using an immersed boundary method, and we present numerical results for both Newtonian and non-Newtonian

In this paper, we develop the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) in mixed formulation applied to parabolic equations with heterogeneous diffusion coefficients. The construction of the method is based on two multiscale spaces: pressure multiscale space and velocity multiscale space. The pressure space is constructed via a set of well-designed local

In this paper the symmetry operators of the fractional Klein-Gordon (KG) equation are found. The generalized fractional Noether’s theorem is used in order to find the conservation laws of the considered equation. Finally, the Chebyshev spectral collocation method is extended to space–time-fractional case for giving some numerical results and conservation laws for the equation.

This paper deals with the robust numerical method for solving the singularly perturbed semilinear partial differential equation with the spatial delay. The quadratically convergent quasilinearization technique is used to linearize the semilinear term. It is formulated by discretization of the solution domain and then replacing the differential equation by finite difference approximation that in turn

In this paper, a fractional-order model for HIV with drug-resistance and CTL immune response is established. Two cases (subsystem with drug-sensitive and subsystem with drug-resistant) are considered. For both subsystems: firstly, the existence and uniqueness of the positive solution is proved; secondly, the sufficient conditions for the stability of the disease-free equilibrium are obtained; finally

This paper attempts to merge the concept of hierarchical finite element analysis (FEA) into isogeometric analysis (IGA). The proposed methodology replaces the traditional grid refinement of IGA with custom enrichment functions. The enrichment functions are properly designed B-Spline wavelets tailored to eliminate scale-coupling terms in the stiffness matrix. In this way, the refined solution is synthesized

This paper is devoted to the development of a mathematical model and its computational analysis targeted at investigating the effects of dual-phase lag on the heating protocol of tumor tissue by the method of electromagnetic hyperthermia. The model comprises two layers, one of them being the vessel layer in which blood flows under the action of a pressure gradient and an external magnetic field, while

Using the finite element approximation of electromagnetic wave propagation problem in frequency domain analysis, we have developed and implemented a finite element model of a terahertz substrate-based wire grid polarizer in a form of unit cell. The proposed polarization unit cell is considered as a waveguide with a specific boundary condition. The model is implemented by the COMSOL software system

In this study, we present the new generalized derivative and integral operators which are based on the newly constructed new generalized Caputo fractal–fractional derivatives (NGCFFDs). Based on these operators, a numerical method is developed to solve the fractal–fractional differential equations (FFDEs). We approximate the solution of the FFDEs as basis vectors of shifted Legendre polynomials (SLPs)

The paper deals with the reliable solution to the homogenization problem for the scalar heat equation with the uncertain hysteresis Prandtl-Ishlinskii operator. The problem is solved by the so-called worst scenario method. The contribution extends the results of paper Franců (2017), to the corresponding homogenization problem.

Computational hemodynamics (CHD) is a promising engineering technique that has allowed doctors to learn a lot about patients’ conditions in various diseases such as cardiovascular disease (CVD) and even surgery. In industrialized countries, hypertension is becoming a widespread public health issue, resulting in death in extreme cases. A successful method for investigating hypertension in both diastolic

In this work we consider an extension of a recently proposed structure preserving numerical scheme for nonlinear Fokker–Planck-type equations to the case of nonconstant full diffusion matrices. While in existing works the schemes are formulated in a one-dimensional setting, here we consider exclusively the two-dimensional case. We prove that the proposed schemes preserve fundamental structural properties

In this paper, we construct and investigate an accurate numerical scheme for solving a class of variable-order (VO) fractional diffusion equation based on the Caputo–Fabrizio fractional derivative. The scheme is presented by using a finite difference method in temporal variable and a local discontinuous Galerkin method (LDG) in space. For all variable-order α(t)∈(0,1), we derive the stability and L2

Evolutionary population-based methods have found their applications in dealing with many real-world simulation experiments and mathematical modelling problems. The Moth-flame optimization (MFO) algorithm is one of the swarm intelligence algorithms and it can be used with constrained and unknown search spaces. However, there are still some defects in its performance, such as low solution accuracy, slow

In this paper, we study finite-time (FET) and fixed-time (FDT) bipartite synchronization of complex networks (CNs) with signed graphs. Under the framework of signed graphs, the interactions between nodes can be either collaborative or antagonistic, which are different from the traditional CNs. Two types of control schemes without the sign function are designed to realize FET and FDT bipartite synchronization

Every outbreak of a serious infectious disease has the potential to pose unprecedented challenges to humanity. Understanding how epidemic spreads among populations is a key step in preventing and controlling it to spread. In this paper, for modeling the epidemic spreading and its associated information spreading, we put forward a novel coupled two-layered networking framework. One layer deals with

Dengue fever is a common mosquito-borne viral infectious disease in the world and is widely spread, especially in tropical and subtropical regions. At this moment, one of the best ways to fight the disease is to prevent mosquito bites. In this study, we present a mathematical model that carefully considers personal protection for humans. It is an epidemiological model that translates the dengue disease

A methodology for calibration and validation of material models using more simultaneous experiments is presented. The procedure contains the selection of suitable parameters for identification using a sensitivity analysis, parameters identification, analysis of usability of the material model, and validation of the material model. Three elastoplastic models are evaluated in this study: the bilinear

The paper deals with finite-difference schemes for a three-dimensional diffusion equation with ψ-Caputo derivative with respect to the time and space variables. Theoretical and experimental estimates of accuracy and performance of implicit and splitting schemes are given. Finite-difference schemes are combined with algorithms that accelerate computations on the base of fixed memory principle and expansion

In the investigations presented here, an efficient computing approach is applied to solve Human Immunodeficiency Virus (HIV) infection spread. This approach involves CD4+ T-cells by feed-forward artificial neural networks (FF-ANNs) trained with particle swarm optimization (PSO) and interior point method (IPM), i.e., FF-ANN-PSO-IPM. In the proposed solver FF-ANN-PSO-IPM, the FF-ANN models of differential

Recent studies demonstrate that the density of prey population is not only affected by direct killing by the predator, but the fear in prey caused by predator also reduces it by cutting down the reproduction rate of prey community, and prey shows anti-predator behavior in response to this fear. In this study, we propose a prey–predator model with fear in prey due to predator and anti-predator behavior

Computationally efficient, structure-preserving reduced-order methods are developed for the Korteweg–de Vries (KdV) equations in Hamiltonian form. The semi-discretization in space by finite differences is based on the Hamiltonian structure. The resulting skew-gradient system of ordinary differential equations (ODEs) is integrated with the linearly implicit Kahan’s method, which preserves the Hamiltonian

Lattice Boltzmann method (LBM) scheme is adopted to simulate the heat transfer processes inside isolated phase and three-phase enclosure gas insulated switchgear (GIS) capsules. D2Q9 fluid flow and thermal Lattice Boltzmann equations (LBEs) are solved through streaming and collision processes. Buoyancy force driven by natural convection is considered by the Boussinesq model. Power losses and thermal

This paper presents a novel control approach for a quadrotor unnamed aerial vehicle (QUAV) in the presence of external disturbances. The QUAV system is difficult to control due to the coupling between its attitude and position, and its dynamics subjected to external disturbances. Therefore, an improved fractional-order fast integral terminal sliding mode control (IFOFITSMC) technique is proposed for

Abstaining from a corrector step of SIMPLE-like algorithms, a coupled pressure-based algorithm is designed using a cell-centered finite-volume Δ-approximation on a collocated grid to predict all-speed fluid flows. A consistently formulated cell-face dissipation scheme is invoked to unravel the occurrence of pressure–velocity decoupling. Modified Rusanov, Roe and Lax–Wendroff flux-difference schemes

We compare several lowest-order finite element approximations to the problem of elastodynamics of thin-walled structures by means of dispersion analysis, which relates the parameter frequency-times-thickness (fd) and the wave speed. We restrict to analytical theory of harmonic front-crested waves that freely propagate in an infinite plate. Our study is formulated as a quasi-periodic eigenvalue problem

In this paper we present an algorithm for solving quasi-pentadiagonal Toeplitz linear systems, that is based on Du et al. method (Du et al., 2014) and the Sherman–Morrison–Woodbury inversion formula. All algorithms have been implemented in Matlab and numerical experiments are given in order to illustrate the validity and efficiency of our algorithm. An application of the proposed algorithm to the Lax–Wendroff

The present research work is to put forth the numerical solutions of the nonlinear second-order Lane–Emden-pantograph (LEP) delay differential equation by using the approximation competency of the artificial neural networks (ANNs) trained with the combined strengths of global/local search exploitation of genetic algorithm (GA) and active-set (AS) method, i.e., ANNGAAS. In the proposed ANNGAAS, the

In this article, we explore the pattern formation caused by fractional cross-diffusion in a 3-species ecological symbiosis model with harvesting. Initially, all possible points of equilibrium are established and then by using Routh–Hurwitz criteria stability of an interior equilibrium point is explored. The conditions for Turing instability are obtained by local equilibrium points with stability analysis

Accurate trajectory control of wheeled robot is an unavoidable problem in path planning, especially in the environment of large positioning error. In this paper, by designing the reverse trajectory and using martingale method, the accurate execution of the target trajectory is realized, and the error estimation is given. Finally, through numerical simulation, it is shown that when the observation error

In this paper, an efficient numerical scheme is presented for solving the space fractional nonlinear damped sine–Gordon equation with periodic boundary condition. To obtain the fully-discrete scheme, the modified Crank–Nicolson scheme is considered in temporal direction, and Fourier pseudo-spectral method is used to discretize the spatial variable. Then the dissipative properties and spectral-accuracy

In this article, a mixed element algorithm is presented to look for the numerical solution for a class of nonlinear wave model with the Caputo fractional derivative. By introducing two auxiliary functions and reducing order technique of fractional derivative, the studied model with high-order derivative in time is transformed into a coupled system including three lower order equations. Next, a fully

In this paper, a new SIS (susceptible–infected–susceptible) epidemic model on complex networks with an infective medium is proposed. The infection rate is modified by applying the theory of probability. By using mean-field approximation, iterative analysis method and mathematical analysis, the epidemic threshold, stabilities of the disease-free equilibrium and the endemic equilibrium are studied. Moreover

A predator–prey model with functional response Holling type II, Allee effect in the prey and a generalist predator is considered. It is shown that the model with strong Allee effect has at most two positive equilibrium points in the first quadrant, one is always a saddle point and the other exhibits multi-stability phenomenon since the equilibrium point can be stable or unstable. The model with weak

This paper presents a stabilization technique for the finite element modeling of contact-impact problems of elastic bars via a bi-penalty method for enforcing contact constraints while employing an explicit predictor–corrector time integration algorithms. The present proposed method combines three salient features in carrying out explicit transient analysis of contact-impact problems: the addition

In recent years there is a vast application of conjugate gradient methods to restore the disturbed signals in compressive sensing. This research aims at developing a scheme, which is more effective for restoring disturbed signals than the popular PCG method (Liu & Li, 2015). To realize the desired goal, a new conjugate gradient approach combined with the projection scheme of Solodov and Svaiter [Kluwer

We will introduce Euler–Maruyama approximations given by an orthogonal system in L2[0,1] for high dimensional SDEs, which could be finite dimensional approximations of SPDEs. In general, the higher the dimension is, the more one needs to generate uniform random numbers at every time step in numerical simulation. The schemes proposed in this paper, in contrast, can deal with this problem by generating

This paper investigates a dual-channel supply chain (SC) composed of a manufacturer and retailer in which the manufacturer confronts random yield issues. Since supply uncertainty may lead to a production shortage, the manufacturer faces the problem of allocating the products to traditional/online channels. To address this problem, a novel product-allocation policy is developed in which the limited

In this paper, we apply the Z-type control method to a crop-pest–natural enemy model. We consider the indirect Z-controller in the natural enemy population and investigate the mathematical properties of the model. Furthermore, our analytical results are also numerically validated. Our paper supports that the pest population can be controlled by using an indirect Z-control mechanism in the natural enemy

In this paper, a new dynamic mathematical model describing leadership emergence or disappearance in agent based networks is proposed. Through a generalised Verhulst–Lotka–Volterra model, a triad of agents operates in a market where each agent detains a quota. The triad is composed of a leader, who leads communication, and two followers. Communications flows both ways from leader to followers and vice

In this paper, a new (3+1)-dimensional integrable Kadomtsev–Petviashvili equation is developed. Its integrability is verified by the Painlevé analysis. The bilinear form, multiple-soliton, breather and lump solutions are obtained via using the Hirota bilinear method, a symbolic computation scheme. Furthermore, the abundant dynamical behaviors for these solutions are discovered. It is interesting that

Innovation Method is a recognized method for the estimation of parameters in diffusion processes. It is well known that the quality of the Innovation Estimator strongly depends on an adequate selection of the initial value for the parameters when a local optimization algorithm is used in its computation. Alternatively, in this paper, we use a strategy based on a modern method for solving global optimization

The present study focuses on designing the memory-based sampled data control approach to achieve the desired performance from switched-type of neural networks. The overall contribution of the study can be viewed from two directions. The first part is to derive the theoretical-based sufficient stability conditions that ensure the synchronization of uncontrolled and controlled systems. The idea behind

In the present study, a novel numerical method solving a thermoelastic diffusion problem with moving boundary is presented. Since the thermoelastic diffusion system is composed of three coupled differential equations, we propose an uncoupled numerical method to obtain an approximate numerical solution with quadratic convergence order in time and space. The error estimate in Sobolev space and order

The success of the shooting of a moving vehicle can be achieved by providing barrel stabilization. In the meantime, it is necessary barrel angle must be positioned is instantaneously calculated accurately. In this paper, the required barrel elevation angle was calculated via artificial neural networks and the shooting success to a fixed target from a moving tank was investigated. For this purpose,

In this paper, a novel iterative algorithm is developed to solve second-order nonlinear singular boundary value problem, whose solution exactly satisfies the Robin boundary conditions specified on the boundaries of a unit interval. The boundary shape function is designed such that the boundary conditions can be fulfilled automatically, which renders a new algorithm with the solution playing the role

The letter aims to generalize the second KP equation to a new one which still possesses a trilinear form. We construct Wronskian determinant solutions, based on its associated trilinear equation, instead of a Hirota bilinear form. Multi-soliton solutions are generated from the presented Wronskian formulation with higher-order dispersion relations. It is then shown that the extended second KP equation

We study the dynamic behavior of a thermoelastic diffusion beam with rotational inertia and second sound, clamped at one end and free to move between two stops at the other. The contact with the stops is modeled with the normal compliance condition. The system, recently derived by Aouadi (2015), describes the behavior of thermoelastic diffusion thin plates under Cattaneo’s law for heat and mass diffusion

In this paper, we explore the effect of the stochastic environmental fluctuations on the dynamics of an HIV system with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity. First, the existence and uniqueness of the global positive solution and the stochastically ultimate boundedness of the stochastic HIV system are discussed. Then, by constructing a series

In this paper, a homogeneous diffusive plant–herbivore model with toxin-determined functional response subject to the homogeneous Neumann boundary condition in the one dimensional spatial open bounded domain is considered. By using Hopf bifurcation theorem and steady state bifurcation theorem due to Yi et al. (2009), we are able to show the existence of Hopf bifurcating periodic solutions (spatially

In this paper, we study the generalized time fractional Burgers equation, where the time fractional derivative is in the sense of Caputo with derivative order in (0,1). If its solution u(x,t) has strong regularity, for example u(⋅,t)∈C2[0,T] for a given time T, then we use the L1 scheme on uniform meshes to approximate the Caputo time-fractional derivative, and use the local discontinuous Galerkin

In this paper the generalized outer synchronization between two coupled dynamical networks is investigated. Combining the advantages of adaptive control technique and stochastic coupling method, a new stochastically adaptive coupling method is proposed. We show, both analytically and numerically, that the generalized outer synchronization can be achieved by using the adaptive stochastic coupling. Particularly

This paper presents a new predictor–corrector numerical scheme suitable for fractional differential equations. An improved explicit Atangana–Seda formula is obtained by considering the neglected terms and used as the predictor stage of the proposed method. Numerical formulas are presented that approximate the classical first derivative as well as the Caputo, Caputo–Fabrizio and Atangana–Baleanu fractional

A particular case of the Hermite interpolation method, namely the two-point Taylor formula, is utilized to construct a numerical technique for solving Fredholm integral equations (FIEs) of the second kind. This method can be applied to approximate the solution of both linear and nonlinear FIEs, and systems of nonlinear FIEs. The sufficient conditions to guarantee the convergence of the proposed method