First Difference Research Articles

Dirichlet systems with discrete relativistic operator

AbstractWe are concerned with Dirichlet systems involving the relativistic discrete operator Here, for , we denote by the forward difference operator. Besides a “universal” existence result for a system with a general nonlinearity, we obtain multiplicity of solutions for systems with parameterized nonlinearities. Our approaches mainly rely on Brouwer degree arguments and critical point theory for convex, lower semicontinuous perturbations of ‐functionals.

Discrete [formula omitted] remainder stability of first and second order schemes for a Volterra integro-differential equation

This work investigates the discrete L1 remainder stability of first and second order schemes for a Volterra integro-differential equation, where the backward Euler and backward difference formula schemes are applied in combination with first and second order convolution quadrature for approximating the integral term, respectively. By Hardy’s inequality and complex analysis techniques to accommodate the singularity of generating functions, we prove the long-time L1 remainder stability of numerical solutions of two schemes, which characterizes the long-time behavior of numerical solutions and indicates the preservation of asymptotically periodic stability of numerical schemes as continuous problems. Numerical experiments are performed to substantiate the theoretical analysis.

Necessary and sufficient optimal control conditions for networked control systems with input delay and Markovian packet dropouts

AbstractThis article studies the optimal control for networked control systems (NCSs) subject to Markovian packet dropouts and input delay. In this scenario, Markovian packet dropouts occur in two channels, that is, from sensor to controller and from controller to actuator. Meanwhile, the input delay arises in the channel from controller to actuator. The contributions of this paper are as the following two aspects: Firstly, based on Pontryagin's maximum principle, the solution to the forward and backward stochastic difference equations (FBSDEs) is obtained. Secondly, in virtue of the obtained solution to the FBSDEs, sufficient and necessary optimal control conditions are derived and the explicit expression of the optimal controller is presented. The validity of the results is illustrated by numerical examples.

Analysis and simulation of vehicle following behavior with consideration of multiple time delays

With the application of intelligent transportation system, drivers can receive more traffic status information in the process of driving, but they may have multiple time delays when they are presented with different information. As a result, to further research the influence of multiple time delays on vehicle following behavior, this study comes up with a modified car following model, which takes into account multiple time delays in sensing both distance and velocity information, based on the backward looking and velocity difference model. The linear stability theory is used to explore the influence of multiple time delays on the stability of the extended model. Different nonlinear equations are derived using nonlinear theory, which include Burgers, Korteweg–de Vries, and Modified Korteweg–de Vries equations and are used to depict triangular wave, soliton wave and kink–antikink wave corresponding to stable, metastable and unstable regions respectively. In the end, numerical simulation is used to further study the improved model to depict the dynamic evolution of traffic stream. The results display that the improvement of time delay in sensing distance can induce traffic congestion, conversely, the time delay in sensing velocity offsets the negative effect of time delay in sensing distance. The theoretical results and numerical simulation results are consistent with each other.

Stochastic linear quadratic optimal control problem with terminal state constraints

AbstractThis paper addresses the stochastic linear quadratic (LQ) control problem with first‐ and second‐order moment constraints on the terminal state. The problem is a modified version of the optimal covariance control problem, where the terminal state is steered to a given probability distribution. Studying a multiplicative‐noise stochastic system rather than an additive‐noise system is a salient feature. Unlike the existing ideas in the optimal steering, by using the Lagrange multipliers method and establishing the stochastic maximum principle, our problem is converted into solving forward–backward stochastic difference equations (FBSDEs), which is a special stochastic two‐point boundary‐value problem (TPBVP). We provide the optimal closed‐loop controller and necessary and sufficient solvability conditions by developing a nonhomogeneous relationship between the optimal state and costate in FBSDEs. Finally, numerical examples are given to demonstrate our results.

Decentralized Output-Feedback Control With Asymmetric One-Step Delayed Information

This paper considers the decentralized LQG control problem for discrete-time decentralized system controlled by two players. In this scenario, player 1 shares a unit delayed observations and control inputs with the controller of player 2, whereas due to the limiting capacity, the controller of player 1 cannot obtain the observations and control inputs of player 2 which leads to the asymmetric one-step delay information. It should be emphasized that this structure makes the classical separation principle fail. Under the assumption of linear control strategies, we derive the optimal estimators based on asymmetric information. In virtue of the Pontryagin's maximum principle, the optimal explicit decentralized controllers are obtained by solving the forward and backward stochastic difference equations (FBSDEs). It is noted that the control gains are coupled with the estimation gains. Moreover, the estimation gains satisfy the forward Riccati equations and the control gains follow the backward Riccati equations which cannot be solved simultaneously. To this end, we present iterative solutions to the coupled forward and backward Riccati equations. Finally, a sufficient condition for the stabilization problem is given in terms of the coupled algebraic Riccati equations. Numerical examples are illustrated to show the effectiveness of the proposed algorithm.

Modelling Infectious Disease Dynamics: A Robust Computational Approach for Stochastic SIRS with Partial Immunity and an Incidence Rate

For decades, understanding the dynamics of infectious diseases and halting their spread has been a major focus of mathematical modelling and epidemiology. The stochastic SIRS (susceptible–infectious–recovered–susceptible) reaction–diffusion model is a complicated but crucial computational scheme due to the combination of partial immunity and an incidence rate. Considering the randomness of individual interactions and the spread of illnesses via space, this model is a powerful instrument for studying the spread and evolution of infectious diseases in populations with different immunity levels. A stochastic explicit finite difference scheme is proposed for solving stochastic partial differential equations. The scheme is comprised of predictor–corrector stages. The stability and consistency in the mean square sense are also provided. The scheme is applied to diffusive epidemic models with incidence rates and partial immunity. The proposed scheme with space’s second-order central difference formula solves deterministic and stochastic models. The effect of transmission rate and coefficient of partial immunity on susceptible, infected, and recovered people are also deliberated. The deterministic model is also solved by the existing Euler and non-standard finite difference methods, and it is found that the proposed scheme forms better than the existing non-standard finite difference method. Providing insights into disease dynamics, control tactics, and the influence of immunity, the computational framework for the stochastic SIRS reaction–diffusion model with partial immunity and an incidence rate has broad applications in epidemiology. Public health and disease control ultimately benefit from its application to the study and management of infectious illnesses in various settings.

A dispersion analysis of uniformly high order, interior and boundaries, mimetic finite difference solutions of wave propagation problems

A preliminary stability and dispersion study for wave propagation problems is developed for mimetic finite difference discretizations. The discretization framework corresponds to the fourth-order staggered-grid Castillo-Grone operators that offer a sextuple of free parameters. The parameter-dependent mimetic stencils allow problem discretization at domain boundaries and at the neighbor grid cells. For arbitrary parameter sets, these boundary and near-boundary mimetic stencils are lateral, and we here draw first steps on the parametric dependency of the stability and dispersion properties of such discretizations. As a reference, our analyses also present results based on Castillo-Grone parameters leading to mimetic operators of minimum bandwidth that have been previously applied in similar physical problems. The most interior parameter-dependent mimetic stencils exhibit a specific Toeplitz-like structure, which reduces to the standard central finite difference formula for staggered differentiation at grid interior. Thus, our results apply to the whole discretization grid. The study done for the 1-D problem could be applied to the discretization of a free surface boundary condition along an orthogonal gridline to this boundary.

Analysis of Fractional Linear Multi-Step Methods of Order Four from Super-Convergence

We analyze two implicit fractional linear multi-step methods of order four for solving fractional initial value problems. The methods are derived from the Grunwald-Letnikov approximation of fractional derivative at a non-integer shift point with super-convergence. The weight coefficients of the methods are computed from fundamental G unwald weights, making them computationally efficient when compared with other known methods of order four. We also show that the stability regions are larger than that of the fractional Adams-Moulton and fractional backward difference formula methods. We present numerical results and illustrations to verify that the theoretical results obtained are indeed satisfied.

Numerical treatment of time-fractional sub-diffusion equation using p-fractional linear multistep methods

In this paper, a kind of the differential equation including a time-fractional sub-diffusion equation is considered. Through this memorandum, a well-known technique, in the time direction is adopted by the p-fractional linear multistep method (p-FLMM) according to the q-fractional backward difference formula (q-FBDF) of implicit type for q = 1, 2, 3, and the spatial direction is approximated by the second-order central difference method. The stability properties of the proposed method can be investigated in combination with the Fourier technique and Z -transformation and also its convergence is studied by using the truncated error maximum. It is shown that the method is unconditionally stable and the orders of convergence are O ( τ p + h 2 ) for 1 ≤ p ≤ 4 , in which p is the order of accuracy in the time direction and τ and h determine temporal and spatial stepsizes, respectively. Some numerical experiments are included to demonstrate the validity and applicability of the scheme.

Parameter estimation for unsteady MHD oscillatory free convective flow of generalized second grade fluid with Hall effects and thermal radiation effects

This work first establishes an unsteady magnetohydrodynamic (MHD) oscillatory free convection flow model of the generalized second grade fluid with Hall heat and mass transfer effect in a straight rectangular duct. A fast second-order spectral method with fractional backward difference formula (FBDF) is proposed to obtain the numerical solution of the established model. The distribution of the velocity and the temperature fields is discussed, and the effect of each parameter on the velocity and temperature fields is shown through graphical experiments. Moreover, in order to avoid the problems of slow computational speed and low accuracy of traditional numerical methods, new fractional physics-informed neural networks (PINNs) are proposed for the multi-parameter estimation of this model. At the same time, a comparative study of our method with the Bayesian method is presented. Experimental results show that fractional PINNs is more effective for multi-parameter estimation problems and get better accuracy at the same number of parameters.

A Second-Order Scheme for the Generalized Time-Fractional Burgers' Equation

Abstract A second-order numerical scheme is proposed to solve the generalized time-fractional Burgers' equation. The time-fractional derivative is considered in the Caputo sense. First, the quasi-linearization process is used to linearize the time-fractional Burgers' equation, which gives a sequence of linear partial differential equations (PDEs). The Crank–Nicolson scheme is used to discretize the sequence of PDEs in the temporal direction, followed by the central difference formulae for both the first and second-order spatial derivatives. The established error bounds (in the L2− norm) obtained through the meticulous theoretical analysis show that the method is second-order convergent in space and time. The technique is also shown to be conditionally stable. Some numerical experiments are presented to confirm the theoretical results.

Perceived stress and psychosomatic complaints in Swedish youth

Abstract Background Psychosomatic complaints are common in youth, and are often assumed to reflect stress. Previous studies have reported associations between perceived stress and psychosomatic complaints. The current study extends this research by examining the longitudinal links between perceived stress and psychosomatic complaints. Methods The data was derived from two survey waves of the Swedish cohort study Futura01, with participants aged ∼17-18 in 2019 (t1) who were followed up in 2022 (t2; n = 2708). Perceived stress was measured by Cohen's Perceived Stress Scale (PSS-4). Psychosomatic complaints were captured by three items on the frequency of stomach ache, headache and sleeping problems, which were added to an index. Sex stratified linear regression analyses were performed, controlling for parental education and parental country of birth, based on information from official registers. The longitudinal analyses were carried out using the first difference (FD) approach, regressing the change in psychosomatic complaints on the change in perceived stress. Results Females reported higher levels of stress and of psychosomatic complaints than males at both time points. There were cross-sectional associations between perceived stress and psychosomatic complaints at t1 (females: b = 0.40, 95% CI 0.36, 0.45; males: b = 0.33, 95% CI 0.29, 0.38) and at t2 (females: b = 0.40, 95% CI 0.36, 0.45; males: b = 0.33, 95% CI 0.29, 0.38). The FD analyses showed that increases in perceived stress were associated with increases in psychosomatic complaints (females: b = 0.19, 95% CI 0.15, 0.23; males: b = 0.19, 95% CI 0.14, 0.23). Conclusions This study provides further empirical support for the assumption that psychosomatic complaints can be regarded as stress-related. Decreasing stress and strengthening young people's resources and strategies to cope with stress may thereby help to reduce the risk of developing psychosomatic complaints. Key messages • Psychosomatic complaints are responsive to perceived stress and can thus be regarded as stress-related. • Reducing stress and strengthening coping resources may increase well-being in youth.

Decentralized control for discrete‐time mean‐field systems with multiple controllers of delayed information

AbstractIn this paper, the finite horizon asymmetric information linear quadratic (LQ) control problem is investigated for a discrete‐time mean field system. Different from previous works, multiple controllers with different information sets are involved in the mean field system dynamics. The coupling of different controllers makes it quite difficult in finding the optimal control strategy. Fortunately, by applying the Pontryagin's maximum principle, the corresponding decentralized control problem of the finite horizon is investigated. The contributions of this paper can be concluded as follows: For the first time, based on the solution of a group of mean‐field forward and backward stochastic difference equations (MF‐FBSDEs), the necessary and sufficient solvability conditions are derived for the asymmetric information LQ control for the mean field system with multiple controllers. Furthermore, by the use of an innovative orthogonal decomposition approach, the optimal decentralized control strategy is derived, which is based on the solution to a non‐symmetric Riccati‐type equation.

Trust and Psychosomatic Complaints in Adolescence: Findings From a Swedish Cohort Study.

Objectives: To examine the cross-sectional and longitudinal associations between generalised and institutional trust and psychosomatic complaints in mid and late adolescence. Methods: Data were derived from the Swedish cohort study Futura01, using survey information collected amongst 3,691 grade 9 students (∼15-16years, t1) who were followed-up 2years later (∼17-18years, t2). Registry information on sociodemographic characteristics was linked to the data. Linear regression analyses were performed. The longitudinal analyses applied the first difference (FD) approach as well as the lagged dependent variable (LDV) approach. Covariates included gender, family type, parental education, parental country of birth, and upper secondary programme. Results: Higher levels of generalised and institutional trust were cross-sectionally associated with lower levels of psychosomatic complaints at both time points. The FD analyses showed that increases in generalised and in institutional trust between ages 15-16 and 17-18years were associated with corresponding decreases in psychosomatic complaints. The LDV analyses demonstrated reciprocal temporal associations between trust and psychosomatic complaints. Conclusion: The findings indicate that trust is a social determinant of psychosomatic complaints in adolescents, but also that health may affect trust.

Second-order efficient algorithm for coupled nonlinear model of groundwater transport system

In this paper, an efficient modified two-grid block-centered finite difference algorithm with second-order backward difference formula is presented for coupled nonlinear reaction-diffusion equations of the solutes in the groundwater flow. The main steps of the modified two-grid algorithm include dealing with a small-scale nonlinear problem on the coarse grid with a large time step size and then dealing with a large-scale linear problem on the fine grid with a smaller time step size base on the second-order backward difference formula. Moreover, the theoretical analysis illustrates that the modified two-grid algorithm is able to maintain second convergence order in space-time domain. Several numerical experiments including a practical example are carried out to support the theoretical results and verify that the modified two-grid block-centered finite difference with second-order backward difference formula algorithm can achieve high efficiency while maintaining the second-order accuracy, meanwhile, has a certain applicable value in actual problem.

Does ESG performance bring to enterprises’ green innovation? Yes, evidence from 118 countries

Research background: The sustainable development and innovation economics theory and related literature place a lot of emphasis on the relationship between environment, society, and governance (ESG) and green innovation. Purpose of the article: The purpose of this paper is to understand what the factors are that influence green innovation and why there is a big disparity in green innovation capabilities between nations. In addition, this paper aims to investigate the impact of ESG performance of green innovation by using unbalanced panel data covering 118 sample countries during the period of 1999–2019. Methods: Panel fixed effect model; Instrumental variable (IV) method; First-differencing (FD) method; Kinky least-squares (KLS) approach. Findings & value added: ESG performance provides evidence for its positive and significant impact on such innovation. Among the ESG factors, governance seems to have the most important influence on green innovation. Moreover, the positive influence of ESG performance is more evident in higher income and wealthy nations. Furthermore, we also conclude that ESG performance can affect green innovation through FDI, human capital, financial development and trade openness. These conclusions hold up after a number of robustness tests and taking into account any potential endogenous issues. Overall, policymakers should pay close attention to the findings.

Numerical Mechanistic Modelling of Drug Release from Solvent-Removal Zein-Based In Situ Gel.

The development of effective drug delivery systems remains a focus of extensive research to enhance therapeutic outcomes. Among these, in situ forming gels (ISG) have emerged as a promising avenue for controlled drug release. This research focuses on the mathematical modeling of levofloxacin HCl (Lv) release from zein-based ISG using the cup method, aiming to mimic the environment of a periodontal pocket. The drug release behavior of the ISGs was investigated through experimental observations and numerical simulations employing forward and central difference formula. Notably, the experimental data for drug release from the 20% w/w zein-based ISG formulations closely aligned with the simulations obtained from numerical mechanistic modeling. In summary, 20% w/w zein-based ISG formulations demonstrated nearly complete drug release with the maximum drug concentration at the edge of the matrix phase values consistently around 100-105%, while 25% w/w zein-based ISG formulations exhibited somewhat lower drug release extents, with values ranging from 70-90%. Additionally, the rate of drug transport from the polymer matrix to the external phase influenced initial release rates, resulting in a slower release. The utilization of glycerol formal as a solvent extended drug release further than dimethyl sulfoxide, thanks to denser matrices formed by high-loading polymers that acted as robust barriers to solvent removal and drug diffusion. Furthermore, UV-vis imaging was utilized to visualize the matrix formation process and solvent diffusion within the ISGs. The imaging results offered valuable insights into the matrix formation kinetics, controlled drug release mechanisms, and the influence of solvent properties on drug diffusion. The combination of mathematical modeling and experimental visualization provides a comprehensive understanding of drug release from zein-based ISGs and offers a foundation for tailored drug delivery strategies.

A SAV finite element method for the Cahn–Hilliard equation with dynamic boundary conditions

In this paper, we propose a SAV method for the Cahn–Hilliard type phase field model with new dynamic boundary conditions. By using the continuous finite element method in space and the backward difference method in time, the fully discrete numerical schemes preserving the energy law are constructed. Numerical examples show that the proposed scheme can simulate the phase field model well even in a relatively rough grid.

Two fast and unconditionally stable finite difference methods for Riesz fractional diffusion equations with variable coefficients

In this paper, for variable coefficient Riesz fractional diffusion equations in one and two dimensions, we first design a second-order implicit difference scheme by using the Crank-Nicolson method and a fractional centered difference formula for time and space variables, respectively. With the compact operator acting on, a novel fourth-order finite difference scheme is subsequently constructed. Solvability, stability and convergence of these schemes are theoretically analyzed. For these discretized linear systems, the fast implementation with preconditioners based on sine transform is proposed, which has the computational complexity of O(nlog⁡n) per iteration and the memory requirement of O(n), where n represents the total number of the spatial grid nodes. Finally, numerical experiments are performed to illustrate the preciseness and effectiveness of these new techniques.