Multistep Methods Research Articles

On a holistic investigation of implicit/explicit/semi-implicit GS4-I framework and time step control for unsteady fluid dynamics

Purpose This paper aims to design and analyze implicit/explicit/semi-implicit schemes and a universal error estimator within the Generalized Single-step Single-Solve computational framework for First-order transient systems (GS4-I), which also fosters the adaptive time-stepping procedure to improve stability, accuracy and efficiency applied for fluid dynamics. Design/methodology/approach The newly proposed child-explicit and semi-implicit schemes emanate from the parent implicit GS4-I framework, providing numerous options with flexible and controllable numerical properties to the analyst. A universal error estimator is developed based on the consistent algorithmic variables and it works for all the developed methods. Applications are demonstrated by merging the developed algorithms into the iterated pressure-projection method for incompressible Navier–Stokes equations. Findings The child-explicit GS4-I has improved solution accuracy and stability properties, and the most stable option is the child explicit GS4-I(0,0)/second-order backward differentiation formula/Gear’s methods, which is new and novel. Numerical tests validate that the universal error estimator emanating from implicit designs works well for the newly proposed explicit/semi-implicit algorithms. The iterative pressure-correction projection algorithm is efficiently fostered by the error estimator-based adaptive time-stepping. Originality/value The implicit/explicit/semi-implicit methods within a unified computational framework are easy to implement and have flexible options in practical applications. In contrast to traditional error estimators, which work only on an algorithm-by-algorithm basis, the proposed error estimator is universal. They work for the entire class of implicit/explicit/semi-implicit linear multi-step methods that are second-order time accurate. Based on the accurately estimated local error, balance amongst stability, accuracy and efficiency can be well achieved in the dynamic simulation.

Pendulum between two springs using Ms- DTM

Abstract This study provides a comprehensive analysis of a pendulum system suspended between two horizontal springs, focusing on its dynamic behavior and the application of advanced mathematical methods. The research begins by formulating the Lagrangian of the system, which serves as the foundation for deriving the equations of motion, offering a rigorous mathematical framework for understanding the system’s dynamics. The nonlinear equations of motion are then solved using the multi-step differential transformation method (Ms-DTM), whose accuracy and effectiveness are evaluated through comparison with the well-established Runge–Kutta method. This comparative analysis highlights the strengths and limitations of each numerical approach in managing the complexity of the system. The study also includes a series of simulated plots that depict the system’s behavior under various initial conditions and parameter settings. These visualizations provide valuable insights into the system’s dynamic responses, revealing phenomena such as chaotic motion and periodic oscillations. The results underscore the utility of sophisticated mathematical methods in addressing complex physical problems and enhancing our understanding of nonlinear dynamic systems.

Reduction of computational time for structural optimisation and application to optimisation of structures

ABSTRACT Structural optimization method takes more computational time because it performs iterative calculation to obtain the optimal value. In particular, the larger the number of elements, the higher the accuracy of the solution, which takes more time. In this study, the superelement method and the static condensation method were used to solve this computational time problem. However, since the general static condensation method generates many equations during the condensation process, the computational time was shortened by developing a multi-step static condensation method that makes the superelement the minimum amount of calculation. In addition, in the optimization process, the calculated stiffness matrix of superelements was reused to shorten the iterative calculation time. In this research model, through the developed method, the computational time was reduced to 39% in the first calculation process and to 60% in the second calculation process to convergence. Therefore, we propose this method as a new optimization process.

High order semi-IMEX BDF schemes for nonlinear partial integro-differential equations arising in finance

In this paper, semi-implicit-explicit (Semi-IMEX) and semi-implicit multistep methods are proposed to solve nonlinear partial integro-differential equations (PIDEs), which describe the option pricing models with transaction costs or illiquid markets under Merton's jump-diffusion process. After spatial differential operators are treated by using finite difference methods and the jump integral is computed by using the composite trapezoidal rule, the consistency error and global error bounds for the semi-IMEX and semi-implicit multistep methods for abstract PIDEs are provided when the nonlinear operator satisfies the boundedness and coercivity conditions. A numerical study is carried out for different option pricing models based on the convergence properties of the schemes and the comparison of the different Greek values. Numerical experiments verify our theoretical results and illustrate the intrinsic nature of the proposed option pricing models under jump-diffusion models with transaction costs or illiquid markets.

Effect of multistage isolation of neutrophils on their counts and viability

Despite numerous separation methods of neutrophils from peripheral blood, isolation of sufficient quantities of high-purity viable cells for quantitative determination of neutrophil cytokines and their mRNA expression still remains an actual issue. The recommended multi-step purification methods significantly prolong the cell isolation process, potentially leading to cell activation or apoptosis and resulting in significant cell loss. Preliminary purification of neutrophils is the most critical stage in terms of time spent, and several additional manipulations with cells. To address this challenge, our study aimed to compare various methods of preliminary neutrophil isolation in order to select the optimal approach to obtaining a sufficient number of viable peripheral neutrophils.We studied the effects of three different protocols for preliminary isolation of cell suspensions: (a) centrifugation of whole blood at a single-step density gradient followed by sedimentation of red blood cells with dextran; (b) centrifugation of whole blood on a double density gradient; (c) rapid isolation of leukocytes using a reagent that promotes red blood cell aggregation. The cell counts and viability of purified neutrophils were tested at the final stage using negative immunomagnetic selection. Our study has shown that the methods used for preliminary neutrophil isolation significantly affect both the number and viability of the cells. The highest number of viable neutrophils was obtained using a conventional method of blood centrifugation at a density gradient followed by dextran sedimentation of red blood cells. However, the three studied methods of preliminary neutrophil isolation did not show statistically significant differences with respect to quantitative yield of viable cells after immunomagnetic isolation. These findings suggest that any of these methods may be applied, depending on capabilities and preferences of the researchers. In summary, our findings confirm previous studies indicating that the multistep process of neutrophil isolation allows for obtaining a high-purity cell suspension (> 99.1%) which can be used in future studies of their cytokine-secreting activity. However, such multi-stage isolation significantly reduces the yield of neutrophils, thus being critical for studying of initially small blood volumes.

Corrigendum to “Analyzing chaotic systems with multi-step methods: Theory and simulations” [Alex. Eng. J. 113 (2025) 516–534

Corrigendum to “Analyzing chaotic systems with multi-step methods: Theory and simulations” [Alex. Eng. J. 113 (2025) 516–534

BERT-Residual quantum language model inspired by ODE multi-step method

BERT-Residual quantum language model inspired by ODE multi-step method

PROCESSING OF MEASUREMENT RESULTS DURING TESTING THE OBJECT UNDER THE INFLUENCE OF A DIRECT LIGHTNING STRIKE

The current state of the problem of evaluating oscillograms during tests for the action of pulsed currents and voltages are analyzed, and the lack of interpretation tools that would meet the requirements of specialized standards for electromagnetic compatibility testing was shown. The program algorithm has been developed for interpreting the results of testing technical objects for resistance to a direct lightning strike in terms of processing oscillograms of various current components. The use of the trapezoidal method for numerical integration enabled the implementation of the algorithm as software for oscillogram interpretation in the Embarcadero RAD Studio XE8 programming environment. Standardized methods for determining pulse front, rise time, and pulse duration were taken into account during the implementation. In addition, the program allows you to determine the charge value and the integral of the current action in accordance with normalized values. Manual adjustment of the analysis interval was added, allowing the filtering of other current components and "noise" effects. The developed software found practical application in the verification testing of artificial lightning current generator complexes. The correctness of the program operation was confirmed by an empirical method. To obtain oscillograms, a measuring shunt with a range of up to 300 kA, lightning component pulse current generators and a simulated test object were used. The analysis was performed for all four components of artificial lightning, including the shortened constant component C*. Comparison of the interpretation results with "manual" analysis proved the high accuracy of the calculation (deviation up to 3%) with significantly less (5-10 times) time costs. Its extensive capabilities make the tool suitable for high-voltage testing and research in power engineering and related fields.

Data enhanced deep transfer learning for health state evaluation of cutting tools

ABSTRACT Health state estimation of cutting tools is a key component for maintaining the reliability and stability of the manufacturing process. Although deep learning (DL) based tool wear indirect monitoring methods have been presented, most of them require a substantial amount of data to avoid high misclassification rates. To this end, this article proposes a novel estimation approach based on data-enhanced deep transfer learning (TL) methodology, which integrates multivariate data enhancements, deep convolution network, and generative adversarial learning for state assessment of the tool wear under small sample size. The proposed method includes three innovative points: 1) a multi-step data enhancement method is employed to augment the wavelet scalogram data as model input; 2) a novel training process is adopted to obtain optimal hyperparameters of TL-AlexNet and TL-VGGNet-16 model; 3) a deep transfer learning model for the enhanced data is presented to adaptively estimate the health state of the cutting tools. The proposed approach only requires a small quantity of data to achieve satisfactory estimation performance compared with other DL methods through experimental validation, and the average prediction accuracy for each stage is greater than 95%, which demonstrates the effectiveness and superiority of the presented model.

Research on Dynamic Modeling and Vibration Characterization of Integrated Bearings

Integrated bearings, characterized by their unique structure, feature an inner ring that is seamlessly integrated with the shaft. This study is based on the theoretical framework of rolling bearing dynamics and considers bearing friction, lubrication, and Hertz elastic contact theory. A dynamic simulation model considering the interaction between the components of the rolling bearing is established. Additionally, a subroutine for calculating the interaction forces between the bearing components was written in C and compiled into a dynamic link library, which was then integrated with the dynamic simulation software. To solve and simulate the dynamics of the integrated bearing model, a sophisticated combination of a refined integration method and the predictor-corrector Adams–Bashforth–Moulton multistep technique was employed. The theoretical analysis offers insights into the vibration characteristics of the integrated bearings across different structural and operational parameters. Results indicate that a judicious selection of parameters, such as the curvature radius ratio of the inner and outer grooves and the gap of the cage pockets, can significantly enhance the bearings’ vibration and noise reduction capabilities. Furthermore, the application of an appropriate axial preload effectively reduces bearing vibrations, and there exists an optimal range of rotational speeds that minimizes these vibrations.

A convergent multi-step efficient iteration method to solve nonlinear equation systems

A convergent multi-step efficient iteration method to solve nonlinear equation systems

Falkner hybrid block methods for second-order IVPs: A novel approach to enhancing accuracy and stability properties

Second-order initial value problems (IVPs) in ordinary differential equations (ODEs) are ubiquitous in various fields, including physics, engineering, and economics. However, their numerical integration poses significant challenges, particularly when dealing with oscillatory or stiff problems. This article introduces a novel Falkner hybrid block method for the numerical integration of second-order IVPs in ODEs. The newly developed method is of order six with a large interval of absolute stability and is implemented using a fixed step size technique. The numerical experiments show the accuracy of our methods when compared with Falkner linear multistep methods, block methods, and other hybrid codes proposed in the scientific literature. This innovative approach demonstrates improved accuracy and stability in solving second-order IVPs, making it a valuable tool for researchers and practitioners.

On generalized asymmetric harmonic oscillator with quadratic nonlinearity within fractional variational principles

This work studies the nonlinear fractional dynamics of asymmetric harmonic oscillators. The classical description of the physical system is generalized using the principles of fractional variational analysis. As a system of two-coupled fractional differential equations with a quadratic nonlinear component, the fractional Euler–Lagrange equations of the motion of the corresponding system are obtained. The Adams–Bashforth predictor-corrector numerical approach is used to approximate the system’s outcomes, which are then simulated comparatively with respect to various model parameter values, including mass, linear and quadratic nonlinear stiffness, and the order of the fractional derivative. The simulations provided the possibility of investigating various dynamical behaviours within the same physical model that is generalized by the use of fractional operators.

Multistep Prediction Analysis of Pure Pursuit Method for Automated Guided Vehicles in Aircraft Industry

The pure pursuit (PP) method has been widely employed in automated guided vehicles (AGVs) to address path tracking challenges. However, the traditional pure pursuit method exhibits certain limitations in tracking performance. For instance, selecting a look-ahead point that is too close can lead to oscillations during tracking, while selecting one that is too far away can result in slow tracking and corner-cutting issues. To address these challenges, this paper proposes a multistep prediction pure pursuit method. First, the look-ahead distance calculation equation is adjusted by incorporating path curvature, allowing it to adaptively adjust according to road conditions. Next, to avoid oscillations caused by constant changes in the look-ahead distance, this paper adopts the prediction concept of model predictive control (MPC) to make multistep predictions for the pure pursuit method. The final input is derived from a linear weighted combination of the multistep prediction results. Simulation analyses and experiments demonstrate that the multistep predictive pure pursuit method significantly enhances the tracking performance of the traditional pure pursuit method.

FRACTIONAL MATHEMATICAL MODEL FOR THE TRANSMISSION DYNAMICS AND CONTROL OF HIV/AIDS

This paper investigates various epidemiological aspects of HIV/AIDS through a fractional-order mathematical model, emphasizing the role of treatment in the disease's transmission dynamics. Given the ongoing global impact of HIV/AIDS, with millions of people affected and significant mortality rates, understanding the complexities of its transmission and control is crucial for effective public health strategies. We establish conditions for the existence and uniqueness of the model’s solutions within the fractional framework and perform a stability analysis of the endemic equilibrium using the Lyapunov function method. Numerical simulations, executed via the fractional Adams–Bashforth–Moulton method, demonstrate the effects of model parameters and fractional-order values on HIV/AIDS dynamics and control. Additional simulations employing surface and contour plots reveal that higher contact rates and reduced treatment efficacy correlate with increased HIV/AIDS prevalence. Our findings suggest that optimizing treatment strategies can significantly lower the prevalence of HIV/AIDS within the population, ultimately contributing to enhanced health outcomes and resource allocation in combating this critical public health issue.

Moral distress, professional value, and vocational choice among senior nursing students: A cross-sectional study.

During clinical placement, nursing students may experience unease and moral distress, which negatively impacts their professional values and vocational choices. However, no instrument exists to measure moral distress in nursing students. Thus, this study constructs measurement items for moral distress and explores the factors that influence the vocational choices of nursing students. The participants were recruited from three universities in South Korea Between September and October 2021. This study was adopted with a convenience sample of 270 Korean fourth-year nursing students who completed their clinical practice at tertiary general hospitals in three provinces in the North, Middle, and South areas of South Korea. Data were collected through a self-administered structured questionnaire. The study developed the items and subscales of the Moral Distress Scale using multistep methods following the recommendations of the Consensus-Based Standards for the Selection of Health Status Measurement Instrument. The study constructed 22 items of the three factors of Moral Distress Scale. The three factors of the Moral Distress Scale were "moral distress by low quality of care," "moral distress by a heavy workload and an insufficient workforce," and "unfair and distrust." The factors influencing the vocational choice of the nursing students were high professional values, intention not to choose nursing as a future career, lacking vision for choosing nursing, democratic family climate, and having at least one parent who was a medical professional. Moral distress in undergraduate nursing students may not influence their intention to choose the nursing profession. Fostering the professionalism and professional values of nursing students through university education curricula may help maintain their professional identity.

Graphene-Inspired Wafer-Scale Ultrathin Gold Films.

As the trajectory toward the graphene era continues, there is a compelling need to harness 2D technology further for the transformation of three-dimensional (3D) materials production and applications. Here, we resolve this challenge for one of the most widely utilized 3D materials in modern electronics─gold─using graphene-inspired fabrication technology that allows us to develop a multistep production method of ultrathin gold films. Such films demonstrate continuous morphology, low sheet resistance (10 Ω/sq), and high transparency (80%), offering opportunities in a variety of technological and scientific sectors. To this end, we demonstrate smart contact lenses and thermal camouflage based on ultrathin gold. Technologically, the record-breaking characteristics of ultrathin gold films open new horizons for flexible and transparent electrodes for photonics and optoelectronics. Most importantly, the demonstration of transferable wafer-scale ultrathin gold changes the paradigm of the field of 2D crystals and dramatically expands the range of available quasi-2D materials.

Oxidation-Resistant Cu-Based Nanowire Transparent Electrodes Activated by an Exothermic Reduction Reaction.

This article describes an approach to making highly stable copper nanowire networks on any type of substrates. These nanostructured materials are highly sought after for, among other applications, the development of next-generation flexible electronics. Their high susceptibility to oxidation in air currently limits their use in the real world. Here, we develop a multistep chemical method to fabricate transparent electrodes (TEs) using Cu-based bimetallic NW networks on various substrates at room temperature. First, we synthesized homogeneous core@shell copper@nickel (Cu@Ni) NWs using a one-pot colloidal approach. After their deposition on a substrate, we exploited the exothermic nature of the reaction between the Ni oxide and hydrazine to eliminate the naturally formed metal oxide moieties and interlock the NW junctions of the network. Electrical measurements, at the single junction level, indicate that the exothermic reaction induces a reduction of resistance by up to 4 orders of magnitude. On a macroscopic scale, the resulting Cu-based NW networks feature an optical transmittance of 80% in the visible region and a sheet resistance of 10 Ω/sq with a record stability of over 2 years. This process offers a simple and efficient strategy for fabricating cost-effective, long-life electronic devices, as illustrated by a proof-of-concept integrating an optimized Cu@Ni-based TE as a flexible transparent heater.

Investigating the effect of an inclined magnetic fieldon heat and mass transmission in turbulent squeeze flowof UCM fluid between parallel plates

This paper investigates the effects of an inclined magnetic field on heat and mass transfer in turbulent squeeze flow of a viscoelastic fluid with an upper-convected Maxwell model. Squeezing flow is an important phenomenon in various industrial and mechanical processes related to flows between parallel surfaces. Mathematical modelling for the law of conservation of mass, momentum, heat and concentration of nanoparticles is executed. The study employs a system of partial differential equations to describe the flow issue. Governing nonlinear partial equations are reduced into nonlinear ordinary differential equations. The modelled equations are then solved numerically by utilizing the efficient Adams-Moulton method of the fourth order based on the shooting technique using the Fortran programming language. Numerical results are compared with another numerical approach and an excellent agreement is observed. The effects of various factors on the non-dimensional velocity, temperature, and concentration patterns are presented using graphs, while tables are used to assess the numerical values of the skin friction, Nusselt and Sherwood numbers. It is found that the temperature profile decreases as the compression parameter increases but increases with an increase in the Eckert number. The results of this study could be useful in designing heat and mass transfer equipment for applications in viscoelastic fluid flows under an inclined magnetic field.

Application Of The Adams Bashforth-Moulton Method To Coffee Production Quantity Approach

Coffee is a type of plantation plant that has long been cultivated so that it has high economic value. Therefore, the authors are interested in approximating the amount of coffee production using the Adams Basforth Moulton method. The Adams Bashforth Moulton method is a way of finding a numerical solution at a certain point of a non-linear differential equation with a known initial value. The differential equation is first solved using the fourth-order Runge Kutta method to obtain four initial solutions which are then substituted into the fourth order Adams Bashforth predictor equation. Furthermore, the approximation value is corrected using the fourth-order Adams Moulton corrector equation. If the relative error is less than the stopping criterion , then the iteration is stopped. The iterations are performed 25 times with an interval of [0,25]. The results of the approximation using the Adams Bashforth Moulton method on the Verhults equation in the approximation show that every year the amount of production increases. The results of the total coffee production in Aceh Province in 2022 will reach 71468 tons and in 2023 it will reach 72966 tons and in 2024 it will reach 74465 tons.