First Difference Research Articles

Local discontinuous Galerkin methods with implicit–explicit BDF time marching for Newell–Whitehead–Segel equations

The Newell–Whitehead–Segel type equations with time-dependent Dirichlet boundary conditions are solved by the local discontinuous Galerkin (LDG) method coupled with the implicit–explicit backward difference formulas (IMEX-BDF). With a suitable setting of numerical fluxes and by the aid of the multiplier technique and the a priori error assumption technique, the optimal error estimate for the corresponding fully discrete LDG-IMEX-BDF schemes is obtained by energy analysis, under the condition τ ≤ C h 1 / s , where h and τ are mesh size and time step, respectively, the positive constant C is independent of h, and s = 1 , … , 5 is the order of the IMEX-BDF method. Numerical experiments are also presented to verify the accuracy of the considered schemes.

Oxygen supplementation and cognitive function in long-COVID.

Patients can experience persistent cognitive complaints and deficits in long-COVID. Inflammation and capillary damage may contribute to symptoms by interfering with tissue oxygenation. This was an exploratory pilot crossover study designed to describe the effects of supplemental oxygen (portable oxygen concentrator, POC) on cognitive performance and peripheral and cerebral oxygen saturation at rest and exercise. Participants with long-COVID (n = 21) were randomized 1:1 to: 1) POC (3h/day) for 2 weeks followed by standard of care (Control) for 2 weeks or 2) Control for 2 weeks then POC (3h/day) for 2 weeks, with a 1-week washout. Cognitive assessment (global cognition [Montreal Cognitive Assessment, MoCA], episodic memory [Hopkins], working memory [Digit Span], executive function [Verbal fluency]) was performed at baseline and after each treatment period. Patient Health Questionnaire (PHQ-9) and Generalized Anxiety Disorder-7 were completed. Peripheral and cerebral oxygen saturation were measured at rest and exercise (treadmill) at baseline and after each treatment period. Statistical analyses were descriptive without formal testing. MoCA scores were similar under POC (26.45±2.31) and Control (26.37±2.85); overall POC-Control difference was -0.090 (95% CI [-1.031, 0.850]). Because of a learning effect, post-hoc analyses were performed for Period 1, where the MoCA score difference was 1.705 [0.140, 3.271]. MoCA subscores suggested better performance with POC for Visuospatial/executive (0.618 [-0.106, 1.342]) and Attention (0.975 [0.207, 1.743]). POC trended to have better scores on Digit Span backward (difference: 0.822 [-0.067, 1.711]) and self-reported depressive symptoms (difference: -1.335 [-3.166, 0.495]). For specific PHQ-9 items, POC tended to have lower (better) scores for Q1 (Little interest/pleasure) and Q7 (Trouble concentrating). Cerebral oxygen saturations at end of exercise showed no difference between POC and Control. Peripheral saturations during exercise were similar under POC and Control (difference: 0.519% [-1.675, 2.714]). An advantage of POC over Control was observed for global cognition, attention, visuospatial/executive performance and depressive symptoms. Results need to be validated in a larger study.

A solving new method for the urea-selective catalytic reduction (SCR) system in a diesel engine using coupled hyperbolic-parabolic partial differential equations (PDEs)

To control the diesel engine urea SCR system with high accuracy, firstly, the partial differential equations of the SCR system are simplified through variable substitution and the method of characteristic lines to eliminate the partial derivative terms of the hyperbolic partial differential equations in the flow direction. The backward difference method is used to solve the problem, and the adaptive time step is adjusted to improve computational efficiency. Secondly, the Levenberg-Marquardt algorithm is applied to identify the model parameters per second based on the 1800-s test bench data. By combining the experimental data with the parameter identification results, this paper calculated the downstream NOx concentration with 99.5 % accuracy. Finally, the 1800s transient test data was applied to a commonly used single-state SCR control model, and cell numbers 1–4 of the cases were numerically simulated. It was found that the reduced-order model had a computation time of 1 s but was less accurate. When the test data was applied to the model presented in this study, the calculation time was 27s, and the model's calculation results show that the average error of the downstream NOx concentration is 16.95 ppm, which is 14.3 ppm lower than that of the two-cell one-state model.

Optimization control strategy for diesel urea-selective catalytic reduction (SCR) urea injection based on the interior point method (IP) + higher order SCR model

In order to ensure that the NOx and NH3 emissions of diesel engines comply with the Euro VII emission standards, this paper optimizes the urea injection using a SCR model combined with the interior point method. First, the equations of the higher-order SCR model were simplified by the variable substitution method and the line method and solved by the backward difference formula to improve computational accuracy. The Levenberg-Marquardt algorithm was used to calibrate the chemical reaction rate parameters to optimize model performance. Second, an optimization cost function was designed to optimize the upstream NH3 concentration in combination with the interior point method and the higher-order SCR model to meet the requirements of Euro VII emission standards. Third, the model effect was verified by performing WHTC hot-start testing on an engine complying with the National VI emission standard. The results show that the average error between the measured NOx concentration and the calculated is 1.49 ppm, which verifies the high accuracy of the model. Finally, the effects of the interior point method, NSGA-II, and MOPSO algorithms in optimizing the upstream NH3 concentration were compared. The results showed that the interior point method outperformed the other algorithms in terms of optimization time and effect, with an optimization time of 149 s, a NOx conversion rate of 97.36 %, and an average downstream NH3 concentration of 4.65 ppm. This achieved a high NOx conversion rate and low NH3 slip in accordance with the requirements of the Euro VII regulation.

Construction of Second-Order Finite Difference Schemes for Diffusion-Convection Problems of Multifractional Suspensions in Coastal Marine Systems

Introduction. This paper addresses an initial-boundary value problem for the transport of multifractional suspensions applied to coastal marine systems. This problem describes the processes of transport, deposition of suspension particles, and the transitions between its various fractions. To obtain monotonic finite difference schemes for diffusion-convection problems of suspensions, it is advisable to use schemes that satisfy the maximum principle. When constructing a finite difference scheme that adheres to the maximum principle, it is desirable to achieve second-order spatial accuracy for bothinterior and boundary points of the domain under study. Materials and Methods. This problem presents certain difficulties when considering the boundaries of the geometric domain, where boundary conditions of the second and third kinds are applied. In these cases, to maintain second-order approximation accuracy, an “extended” grid is introduced (a grid supplemented with fictitious nodes). The guidelineis the approximation of the given boundary conditions using the central difference formula, with the exclusion of the concentration function at the fictitious node from the resulting expressions. Results. Second-order accurate finite difference schemes for the diffusion-convection problem of multifractional suspensions in coastal marine systems are constructed. Discussion and Conclusion. The proposed schemes are not absolutely stable, and a detailed analysis of stability and convergence, particularly concerning the grid step ratio, remains an important problem that the author plans to address in the future.

A priori and a posteriori error estimates for efficient numerical schemes for coupled systems of linear and nonlinear singularly perturbed initial-value problems

This work considers the numerical approximation of linear and nonlinear singularly perturbed initial value coupled systems of first-order, for which the diffusion parameters at each equation of the system are distinct and also they can have a different order of magnitude. To do that, we use two efficient discretization methods, which combine the backward differences and an appropriate splitting by components. Both a priori and a posteriori error estimates are proved for the proposed discretization methods. The developed numerical methods are more computationally efficient than those classical methods used to solve the same type of coupled systems. Extensive numerical experiments strongly confirm in practice the theoretical results and corroborate the superior performance of the current approach compared with previous existing approaches.

Zero-sum games subject to uncertain stochastic noncausal systems considering polynomial control functions

An uncertain stochastic noncausal system (USNS) is an uncertain stochastic singular system that is expected to be regular but not impulse-free. This study investigates zero-sum games (ZSGs) under the constraint of nonlinear uncertain stochastic noncausal systems (USNSs) considering polynomial control functions. Firstly, a method is introduced to convert USNSs into subsystems, including forward uncertain stochastic difference equations as well as backward uncertain stochastic difference equations. Equilibrium equations are then derived to determine the saddle-point equilibrium solution of the zero-sum game (ZSG) for USNSs. Subsequently, a unified framework is developed to find the saddle-point equilibrium and equilibrium value of the ZSG. Additionally, a numerical example and an analysis of the treatment of industrial wastewater are provided to demonstrate the effectiveness of the proposed framework.

Efficient numerical solution of linear Fredholm integro-differential equations via backward finite difference and Nyström methods

Efficient numerical solution of linear Fredholm integro-differential equations via backward finite difference and Nyström methods

Two fast finite difference methods for a class of variable-coefficient fractional diffusion equations with time delay

This paper introduces the fast Crank–Nicolson (CN) and compact difference schemes for solving the one- and two-dimensional fractional diffusion equations with time delay. The CN method is employed for temporal discretization, while the fractional centered difference (FCD) formula discretizes the Riesz space derivative. Additionally, a novel fourth-order scheme is developed using compact difference operators to improve accuracy. The convergence and stability of these schemes are rigorously proven. The discretized systems combining Toeplitz-like structures can be effectively solved by Krylov subspace solvers with suitable preconditioners. Each time level of these methods requires a computational complexity of O(plogp) per iteration and a memory of O(p), where p represents the total number of grid points in space. Numerical examples are given to illustrate both the theoretical results and the computational efficiency of the fast algorithm.

Numerical Analysis of the Discrete, Fractional Order PID Controller Using FOBD Approximation

This paper proposes a methodology of the numerical testing of the discrete, approximated Fractional Order PID Controller (FOPID). The fractional parts of the controller are approximated using the Fractional Order Backward Difference (FOBD) operator. The goal of the analysis is to find the memory length optimum from point of view both accuracy and duration of computations. To do it new cost functions describing both accuracy and numerical complexity were proposed and applied. Results of tests indicate that the optimum memory length lies between 200 and 400. The proposed approach can be also useful to examine of another discrete implementations of a fractional order operator using FOBD.

A comparative study on numerical methods for Fredholm integro-differential equations of convection-diffusion problem with integral boundary conditions

This paper numerically solves Fredholm integro-differential equations with small parameters and integral boundary conditions. The solution of these equations has a boundary layer at the right boundary. A central difference scheme approximates the second-order derivative, a backward difference (upwind scheme) approximates the first-order derivative, and the trapezoidal rule is used for the integral term with a Shishkin mesh. It is shown that theoretically, the proposed scheme is uniformly convergent with almost first-order convergence. Further to improve the order of convergence from first order to second order, we use the post-processing and the hybrid scheme. Two numerical examples are computed to support the theoretical results.

Neoclassical Gravitational Field Theory

This Neoclassical Gravitational Field Theory offers a potential alternative perspective on the nature of gravity by expanding upon Newton’s classical law of gravitation. It seeks to address fundamental questions, such as why gravity functions as it does and why nothing in the universe can escape its influence. This paper explores some of the long-standing mysteries of gravity, including why masses are multiplied in Newton's gravitational formula and why objects accelerate at the same rate in a local gravitational field, regardless of their structure or composition. By presenting a classical framework, this research aims to provoke discussion and encourage further exploration of alternative explanations for gravity, potentially leading to a deeper understanding of both gravity and the universe itself.

Wall-Modeled Large-Eddy Simulation Method for Unstructured-Grid Navier–Stokes Solvers

This paper reports on the implementation and assessment of a wall-modeled large-eddy simulation (WMLES) methodology in an unstructured-grid, node-centered flow solver, FUN3D, that is developed and supported at the NASA Langley Research Center. Finite-volume (FV) and finite-element (FE) discretization schemes considered in the study provide formal second-order spatial accuracy. Large-eddy simulations (LES) resolve large-scale turbulent-flow features, and small-scale effects are modeled using the Vreman subgrid-scale model. At solid-wall boundaries, a shear-stress model is employed to provide a proper boundary-flux closure. The nonlinear equations are integrated in time using either an optimized backward difference formula or an implicit multistage Runge–Kutta temporal scheme. The implicit equations at each time step are solved by strong nonlinear iteration schemes. WMLES demonstrations are shown for two high-lift configurations, namely, the McDonnell Douglas 30P30N multi-element airfoil and a NASA High-Lift Common Research Model. Results show that the WMLES approaches implemented in the FV and FE discretization methods produce consistent solutions and are capable of capturing key aerodynamic characteristics and flow structures for high-lift configurations at a wide range of angles of attack, including maximum-lift conditions. In the 30P30N example, correct trends in the variations of integrated aerodynamic forces and moments, surface pressure distributions, and boundary-layer profiles are captured as the Reynolds number is increased.

An approach to mismatched disturbance rejection control for uncontrollable systems

This study focuses on the problem of optimal mismatched disturbance rejection control for uncontrollable linear discrete-time systems. In contrast to previous studies, by introducing a quadratic performance index such that the regulated state can track a reference trajectory and minimize the effects of disturbances, mismatched disturbance rejection control is transformed into a linear quadratic tracking problem. The necessary and sufficient conditions for the solvability of this problem over a finite horizon and a disturbance rejection controller are derived by solving a forward–backward difference equation. In the case of an infinite horizon, a sufficient condition for the stabilization of the system is obtained under the detectable condition. Additionally, in combination with the generalized extended state observer, a controller design method is proposed, and the stability analysis of the system under this controller is presented. This paper details our novel approach to disturbance rejection. Finally, four examples are provided to demonstrate the effectiveness of the proposed method.

Linear quadratic optimal control of stochastic 2-D Roesser models

This paper investigates the linear quadratic (LQ) optimal control problem for the stochastic two-dimensional (2-D) systems governed by Roesser models with multiplicative noise. The main contribution is to give the necessary and sufficient optimality condition by proposing a set of novel forward and backward stochastic partial difference equations (FBSPDE), and to further present the explicitly optimal feedback control laws on the finite horizon and on the infinite horizon based on the Riccati-like difference equations and the algebraic equation, respectively. Several numerical simulations are provided to illustrate the performance of the designed controllers.

A sixth-order finite difference method for the two-dimensional nonlinear advection diffusion reaction equation

A novel higher-order finite difference method is developed to solve the two-dimensional nonlinear advection diffusion reaction equation. Firstly, a new five-point sixth-order finite difference scheme is proposed to discretize spatial derivatives and the sixth-order backward difference method is applied to teat temporal derivative. As a result, a new fully implicit scheme with sixth-order accuracy in both time and space is proposed. Subsequently, for the calculation of the starting step of the sixth-order backward difference method, the Crank-Nicolson method combined with the Richardson extrapolation technique is employed to obtain the equivalent temporal accuracy as the main scheme. Finally, the accuracy and reliability of the presented method are validated through various numerical examples.

A second order difference method combined with time two-grid algorithm for two-dimensional time-fractional Fisher equation

In this paper, a finite difference (FD) scheme based on time two-grid algorithm is proposed for solving the two-dimensional time-fractional Fisher equation (2D-TFFE). Firstly, the Caputo fractional derivative and the spatial derivative are discretized by the L 2 − 1 σ formula and the central difference formula, respectively. In order to improve the efficiency of computation, the time two-grid algorithm is then constructed. Secondly, based on the cut-off function technic, stability and convergence of the time two-grid FD scheme are obtained by the energy method, and the global convergence order is O ( τ F 2 + τ C 4 + h x 2 + h y 2 ) , where τ F and τ C represent time-step sizes on the fine and coarse grid, respectively, while h x and h y represent the space-step sizes. Finally, numerical experiments are presented to show the feasibility and efficiency of the algorithm.

Model to identify comfortable cloth fabric for human body during thermal stress due to physical exercise

Physical exercise enhances heat generation in human skin and subcutaneous tissues causing thermal stress. This thermal stress causes discomfort in the human body and deteriorates the physical performance of the human subjects. Appropriate choice of cloth for outer covering of human body is necessary to prevent this to provide comfort during the thermal stress. A mathematical model is proposed in this study to analyze the thermal stresses in human skin and subcutaneous tissues covered with various different cloth fabrics. The model considers four compartments namely cloth, epidermis, dermis, subcutaneous tissues. The bioheat equation along with appropriate boundary condition is employed in this model for one dimensional unsteady state case. The numerical simulation is performed using forward and central finite difference formulas. The findings have been utilized to examine how different types of fabric impact thermal stress experienced by the layers of human skin during physical activity. The polyester is found to be superior in comparison to cotton fabric as it shows less thermal stress and thus can be concluded to be more comfortable as a dress material.

Psychosomatic complaints are indicative of stress in young individuals: findings from a Swedish national cohort study.

Psychosomatic complaints are common in youth and are often assumed to indicate stress. Although several studies have confirmed that a cross-sectional association exists, few have empirically investigated whether or not perceived stress influences psychosomatic complaints. The objective of the present study was to build upon previous research by exploring whether changes in perceived stress over time are associated with corresponding changes in psychosomatic complaints. This analytical approach takes unmeasured time-invariant confounding into account, thereby offering more robust evidence for a causal association between the variables under study. Data was derived from the Swedish national cohort study Futura01, with information from 2,708 participants aged 17-18 in 2019 and 20-21 in 2022. Perceived stress was measured by Cohen's Perceived Stress Scale. Psychosomatic complaints were measured by questions on the frequency of stomach aches, headaches and difficulties falling asleep, which were added to an index. Information on gender, parental education, and parental country of birth was derived from registries. Linear regression analyses were conducted and the first difference (FD) approach was used. Perceived stress and psychosomatic complaints exhibited cross-sectional associations at both time points. The FD analyses showed that increases in perceived stress were associated with increases in psychosomatic complaints, and this was the case irrespective of sociodemographic characteristics. This study provides further empirical support for the assumption that psychosomatic complaints can be partially attributed to stress. Societal efforts aimed at reducing stressors and strengthening coping resources and strategies among young people may help mitigate perceived stress and, consequently, the likelihood of developing psychosomatic complaints.

A novel dynamic predictive control model for variable air volume air conditioning systems using deep learning

Model-based predictive control has proven effective for managing indoor temperature and humidity in variable air volume (VAV) air conditioning systems. However, delays in temperature and humidity adjustments in response to changes in internal and external environmental conditions can impede high-performance operation. This study introduces a dynamic predictive control model for the multi-zone indoor temperature and humidity of VAV systems, designed to predict and control these parameters in real-time. Utilizing the RC network two-node wall structure method and backward finite difference scheme, a multi-zone building model is developed. Coupled with a deep fuzzy cognitive map (DFCM) for temperature and humidity prediction, and controlled by a PID controller, the model dynamically regulates the opening degrees of terminal air dampers and chilled water valves. Implemented on a networked control platform in a large commercial building, the model consistently maintained indoor temperature and humidity within ±0.5 °C and ±0.1 g/(kg dry air) of the target values under varying conditions, demonstrating substantial improvements in stability and operational efficiency. The research enhances the predictability and control of HVAC systems through advanced algorithmic integration, improving real-time indoor climate management in complex building environments. This method offers a practical improvement in HVAC control technologies, which could be beneficial for applications in commercial building management systems, providing a useful tool for supporting energy efficiency and sustainability in modern infrastructures.