Multistep Methods Research Articles

Truncation Error of the Network Simulation Method: Chaotic Dynamical Systems in Mechanical Engineering

This article focuses on the study of local truncation errors (LTEs) in the Network Simulation Method (NSM), specifically when using the trapezoidal method and Gear’s methods. The NSM, which represents differential equations through electrical circuit elements, offers advantages in solving nonlinear dynamic systems such as the van der Pol equation. The analysis compares the performance of these numerical methods in terms of their stability and error minimization, with particular emphasis on LTE. By leveraging circuit-based techniques prior to numerical application, the NSM improves convergence. This study evaluates the impact of step size on LTE and highlights the trade-offs between accuracy and computational cost when using the trapezoidal and Gear methods.

Anthropometric profile and dietary intake of amateurs and professional mixed martial arts athletes

Nutritional habits and anthropometric profiles are directly linked to competitive performance; however, there is a great lack of information on amateur or professional mixed martial arts (MMA) athletes outside the competitive period. The aim of this study was to compare food consumption and anthropometric profile of amateur and professional MMA fighters. The sample was composed of 24 male MMA athletes, middleweight category (age: 27.5 ± 5.0 years; body mass: 79.0 ± 12.1 kg; height: 173.5 ± 0.1 cm; %BF: 19.5 ± 4.0 %, BMI: 26.0 ± 2.8 kg/m2). Food consumption was evaluated based on three 24-hour food diaries using the Multi-Step method in a non-competitive period and analyzed using the Dietbox v2.92 software. The professional group was younger (p = 0.001) than the amateur group. Total energy expenditure was similar between amateur (4364 ± 469 kcal) and professional (4312 ± 381 kcal). Amateur and professional reported an energy deficit between the estimated energy requirement and energy intake. Carbohydrate consumption was below the suggested minimum limits (amateur: 3.3 ± 1.6g/kg/day and professional: 3.3 ± 1.4g/kg/day). Protein intake was within the suggested limits (amateur: 1.4 ± 0.9g/kg/day and professional: 1.8 ± 0.8g/kg/day) and lipids presented borderline values about to with concerning the recommendations in the literature (amateur: 0.9 ± 0.6 / g/kg/day and professional: 1.8 ± 0.9 g/kg/day). Amateur and professional athletes did not differ in terms of food consumption and anthropometric profile. Both groups, amateur and professional, demonstrated negative energy balance and inability to reach the suggested levels of macronutrient intake according to the classification. Thus, it is recommended that both MMA groups receive attention regarding nutritional strategies.

Fractional-Order Mathematical Modeling of Methicillin- Resistant Staphylococcus aureus Transmission in Hospitals

This article investigates the environmental contamination and antibiotic exposure effect on the transmission dynamics of the Methicillin-Resistant Staphylococcus aureus (MRSA) model in hospitals using the fractional Adams–Bashforth–Moulton Method (ABMM). This epidemic model simulates the dynamics of patient populations, bacterial contamination, and healthcare worker safety under varying conditions. This model provides critical insights into the interactions between hospital practices, environmental factors, and infection dynamics, demonstrating the importance of symmetry in balancing hospital admission and discharge rates to manage infection spread effectively. The analysis extends to the impact of environmental bacterial density and hospital admission rates on patient colonization. Increasing admission rates introduce more susceptible patients, exacerbating infection spread when bacterial density is high. Conversely, lower admission rates and bacterial density result in a more controlled infection environment. The model further investigates how varying discharge rates influence colonization dynamics, highlighting that effective discharge practices can mitigate infection spread, especially in high-bacterial density scenarios. It must be noted that this model is studied fractionally for the first time. Overall, this model provides critical insights into the interactions between hospital practices, environmental factors, and infection dynamics, offering valuable guidance for infection control strategies and hospital policy formulation. By adjusting fractional order constant (σ) values and analyzing different scenarios, this research aids in understanding and managing bacterial infections in healthcare settings. The proposed method is able to provide the results presented in the figures within this study considering the influence of many factors.

Optimization of thermal performance in hybrid nanofluids for parabolic trough solar collectors using Adams–Bashforth–Moulton method

Solar energy is an environment-friendly renewable energy source that fulfills the energy consumption requirements of the world economy. Concentrated solar power is the most advanced technology that efficiently absorbs concentrated solar energy. This article investigates the solar energy storage and entropy generation in concentrated parabolic trough solar collectors for hybrid nanofluid flow due to a spinning tube inserted at the receiver's center. The effect of copper nanoparticles and multi-walled carbon nanotube mixture is studied using water-based fluid. Also, the influence of an external magnetic field is investigated with thermophoresis and Brownian motion of nanoparticles. The governing equations for the nanofluid flow are derived using the conservation principles of mass, momentum, energy, and concentration with boundary layer assumptions and no-slip boundary conditions. The governing equations are numerically solved using Adam Bashforth and Adam Moulten's fourth-order predictor-corrector numerical scheme along with the shooting approach. The numerical outcomes for the fluid velocity, temperature, Nusselt number, and entropy formation against various influential physical parameters have been discussed using graphs. It is observed that the augmenting Eckert number, thermophoretic diffusion parameter, and Brownian motion parameter escalates the thermal profiles. Also, an escalation of the radiation parameter and Lewis number enhances the Nusselt number. Thermal energy storage in solar collectors utilizing different terminologies is crucial for improving the efficiency and performance of solar thermal collectors.

Multi-step Residual Power Series Method for Solving Stiff Systems

In this paper, an efficient algorithm based on the residual power series method (RPSM) is presented to solve stiff systems of Caputo fractional order. We apply the RPSM on subintervals to get approximate solutions of these types of systems. The RPSM has advantages that it is suitable to solve linear and nonlinear systems and it gives high accurate results. Modifying this technique to multi-step RPSM considerably reduces the number of arithmetic operations and so reduces the time, especially when dealing with Stiff systems. Several numerical examples are given to show the efficiency, simplicity and the accuracy of the proposed method. Comparing classical RPSM with the new multi-step scheme shows that multi-step RPSM controls the convergence behaviour of the stiff systems. That is, the comparison reveals that MS-FRPSM reduces both absolute and residual errors. More iterations and a smaller step size lead to higher accuracy. Moreover, in MS-FRPSM, the intervals of convergence for the series solution will increase.

Fractal-Fractional-Order Modeling of Liver Fibrosis Disease and Its Mathematical Results with Subinterval Transitions

In this paper, we study human liver disease with a different approach of interval-based investigation by introducing subintervals. This investigation may be referred to as a short memory investigation. Such concepts are useful in problems where a transition is observed when transitioning from one subinterval to the other one. We use the classical and fractal-fractional-order derivative in each subinterval. We study the existence of solutions by using Banach’s and Krasnoselskii’s fixed-point theorems. Their stability is analyzed by adopting the Hyers–Ulam (H-U) stability approach. Also, using the extended Adams–Bashforth–Moulton (ABM) method, we simulate the results that visually present the numerical solutions for different fractal-fractional-order values.

ESTIMATION OF OIL SPILLAGE AND SALVAGE REVENUE IN KOKORI OIL FIELD USING NUMERICAL METHODS AND PYTHON ALGORITHM

The study aimed to estimate oil spillage in the Kokori Oil Field, discovered in 1958, using a linear model. The field has 23 oil wells and produced 383 million barrels of oil. A linear model was developed using Python programming, comparing it with the trapezoidal method and salvage revenue. Results showed a linear relationship between oil spill quantity, duration, and mitigation measures. This study provides a valuable model for estimating oil spillage in the Kokori oil field, emphasizing the importance of accurate estimation for environmental and economic purposes. The study presents a comprehensive model for estimating oil spillage in the Kokori oil field, emphasizing the significance of accurate estimation for environmental and economic purposes. The correlation coefficient value supports the model's sufficiency, and the calculated salvage revenue indicates a commendable projected value for the Kokori oil field at its end of use. Salvage revenue is the estimated value of an asset at the end of its useful life, which is crucial in determining the cost of goods sold and depreciation charge. It lowers the asset's cost, influences its usable life, resale value, and replacement cost. Salvage revenue is calculated by subtracting revenue generated without mitigation measures from revenue realized with mitigation measures.

Multi-step Adomian decomposition method for solving a delayed Chikungunya virus system

Multi-step Adomian decomposition method for solving a delayed Chikungunya virus system

The effect of positive and reverse current cycles on the wettability, morphology, and corrosion behaviour of electrodeposited nickel matrix layer

ABSTRACT In this study, Ni-TiO2 coatings were formed using a multi-step pulse method with positive and, in some cases, reverse current steps. All coatings were produced at a current density of 4 A dm−2 and a frequency and duty cycle of 10 Hz and 10%, respectively with a thickness of 30 µm. The results showed that by applying the reverse current cycle, the codeposition of TiO2 particles in the coating decreased and the morphology of the coating became irregular. It was found that the effect of the wetting angle of the coating is greater than the incorporation of TiO2 particles on the corrosion behaviour of the coating. Thus, a coating was created with a positive 4-step pulse current with the lowest amount of TiO2 particles (7.7 vol.%) having the highest resistance against corrosion. The sample had compact morphology and high wetting angle (82.61o֯).

One-shot manufacturable soft-robotic pump inspired by embryonic tubular heart.

Soft peristaltic pumps, which use soft ring actuators instead of mechanical pistons or rollers, offer advantages in transporting liquids with non-uniform solids, such as slurry, food, and sewage. Recent advances in 3D printing with flexible thermoplastic polyurethane (TPU) present the potential for single-step fabrication of these pumps, distinguished from handcrafted, multistep traditional silicone casting methods. However, because of the relatively high hardness of TPU, TPU-based soft peristaltic pumps contract insufficiently and thus cannot perform as well as silicone-based ones. Improving the performance is crucial for fully automated, one-step manufactured soft pumps to lead to industrial use. This study aims to enhance TPU-based soft pumps through bioinspired design. Specifically, it proposed a design inspired by embryonic tubular hearts, in contrast to previous studies that mimicked digestive tracts. The new design facilitated long-axis stretching of an elliptical lumen during non-concentric contractile motion, akin to embryonic tubular hearts. The design was optimized for ring actuators and pumps 3D-printed with shore hardness 85 A TPU filament. The ring actuator achieved over 99% lumen closure with the best designs. The soft pumps transported water at flow rates of up to 218 ml min-1and generated a maximum discharge pressure of 355 mm Hg, comparable to the performance of blood pumps used in continuous renal replacement therapy.

A Six-Point y-Function Hybrid Block Method for Direct Solution of Third Order Ordinary Differential Equations

In this article, a new continuous numerical method was developed for the numerical integration of general third-order initial value problems (IVPs) of ordinary differential equations (ODEs). The method was derived by adopting interpolation and collocation approach using a combination of power series and exponential functions as the basis function for the approximate solution to the ODEs. The approximate solution was interpolated at both nodal and off-nodal points while the differential systems from the approximate solution was collocated at all nodal points to obtain the set of methods with given step-numbers. This derived approach ensured that the hybrid points are obtained at the y-values of the methods. This class of hybrid linear multi-step method satisfied the conditions for usability and accuracy of any given method. These conditions were confirmed by testing the consistency, stability and convergence of the developed method. The method was applied to solve directly linear and non-linear third order ODEs without reduction to system of first-order ordinary differential equations. Results from the computation compared favorably with some existing numerical methods in literature with comparable properties to confirm the superiority of the newly developed method.

Tailoring MnO2 nanowire defects with K-doping for enhanced electrochemical energy storage in aqueous supercapacitors

The fabrication of supercapacitors with outstanding performance is presented with a distinct defect-rich nanostructures. A one-pot, energy-efficient method for synthesizing defective manganese dioxide nanowires doped with potassium (K0.35MnO2) was developed. The introduction of potassium ions at 35 % birnessite resulted in a significant increase in lattice defects and an improvement in conductivity. Addition of KOH induces a phase transition from α-MnO2 to δ-MnO2. These imperfections result in a greater quantity of active sites, which are crucial for the process of energy storage. The K0.35MnO2 structure demonstrates a 405F/g increased capacity at a current density of 1 A/g. The asymmetric supercapacitor (K0.35MnO2/AC) that was manufactured exhibits a capacitance of 106.4F/g when operating at 1 A/g, while maintaining a maximum energy density of 71.5 Wh kg−1 and a power density of 672 W kg−1. Furthermore, 92.7 % of the initial capacitance of the device is retained even after 8,000 cycles at 20 A/g. This study presents novel insights into the production of defective materials for energy storage applications through the utilization of a one-pot process as opposed to the multi-step method. In order to produce high-performance supercapacitors for practical applications, the results indicate that defect engineering is a crucial factor.

Strong stability preserving second derivative multistep methods

Strong stability preserving second derivative multistep methods

Improved gene editing and fluorescent-protein tagging in Aspergillus nidulans using a Golden Gate-based CRISPR-Cas9 plasmid system

CRISPR-Cas9 systems can be used for precise genome editing in filamentous fungi, including Aspergillus nidulans. However, current CRISPR-Cas9 systems for A. nidulans rely on relatively complex or multi-step cloning methods to build a plasmid expressing both Cas9 and an sgRNA targeting a genomic locus. In this study we improve on existing plasmid-based CRISPR-Cas9 systems for Aspergilli by creating an extremely simple-to-use CRISPR-Cas9 system for A. nidulans genome editing. In our system, a plasmid containing both Cas9 and an sgRNA is assembled in a one-step Golden Gate reaction. We demonstrate precise, scarless genome editing with nucleotide-level DNA substitutions, and we demonstrate markerless gene tagging by fusing fluorescent-protein coding sequences to the endogenous coding sequences of several A. nidulans genes. We also describe A. nidulans codon-adjusted versions of multiple recent-generation fluorescent proteins, which will be useful to the wider Aspergillus community.

Development and validation of a questionnaire to evaluate attitude about menstruation among adolescent girls

Abstract: CONTEXT: Cultural influences promote secrecy, making it difficult for girls to openly discuss menstruation. This further impacts their attitude and emotional well-being. Showing adolescent girls the reality of menstruation would give them a clear understanding of menstruation. AIMS: The aim of this study was to develop and validate a questionnaire to evaluate attitude about menstruation among Adolescent girls. SETTINGS: Adolescent girls in Belagavi city. DESIGN: Exploratory study. SUBJECTS AND METHODS: The Adolescent Menstrual Attitude Inventory Questionnaire (AMAI-Q) was developed using a multistep method divided into two phases. Phase I: Concept elicitation, which includes identification of domains and item generation; and expert input, which includes content validation. Phase II: Pilot testing of 11 adolescent girls and reliability calculation using Cronbach’s alpha. STATISTICAL ANALYSIS USED: The content validity index of the questionnaire was calculated, and the reliability of the questionnaire was assessed using Cronbach’s alpha. RESULTS: The content validity of the questionnaire was tested using the content validity index, which was found to be 0.911. Reliability was assessed using Cronbach’s alpha and was found to be 0.818, indicating good reliability. CONCLUSIONS: The proposed questionnaire, AMAI-Q is well-validated, easy to administer, and has good reliability. AMAI-Q will be a suitable scale to evaluate attitude about menstruation among adolescent girls.

A besyian regularisation neural network approach for hepatitis B virus spread prediction and immune system therapy model

The primary aim of the article is to analyze the response of the human immune system when it encounters the hepatitis B virus. This is done using a mathematical system of differential equations. The differential equation system has six components, likely representing various aspects of the immune response or virus dynamics. A Bayesian regularization neural network has been presented in the process of training. These networks are employed to find solutions for different categories or scenarios related to hepatitis B infection. The Adams method is used to generate reference data sets. The back-propagated artificial neural network, based on Bayesian regularization, is trained and validated using the generated data. The data is divided into three sets: 90% for training and 5% each for testing and validation. The correctness and effectiveness of the proposed neural network model have been assessed using various evaluation metrics. The metrics have been used in this study are Mean Square Error (MSE), histogram errors, and regression plots. These measures provide support to the neural network to approximate the immune response to the hepatitis B virus.

About One Multistep Multiderivative Method of Predictor-Corrector Type Constructed for Solving İnitial-Value Problem for ODE of Second Order

Considering the wide application of the initial-value problem for Ordinary Differential Equations second-order with a special structure, here for solving this problem constructed the special Multistep Multiderivative Methods. Many scientists studied this problem , but the most distinguishing is the Ştörmer. To solve this problem here is proposed to use the Multistep Second derivative Method with a special structure. This method has been generalized by many authors, which is called as the linear Multistep Multiderivative Methods with the constant coefficients. Many authors shave shown that the Multistep Second derivative Method can be applied to solve the initial-value problem for ODEs of the first order. Euler himself using his famous method discovered that, in his method when moving from one point to another local truncation errors add up, the results of which reach a very large value. To solve this problem, he suggested using more accurate methods. For this aim, Euler proposed calculating the next term in the Taylor series of the solutions of the investigated problem. Developing this idea and papulation of the Multistep Multiderivative Methods here to solve the named problem it is suggested to use MultistepThriedderivative Methods, taking into account that methods of this type are more accurate. For the demonstration above, receiving results here have constructed some concrete methods. Also by using some of Dahlquist’s and Ibrahimov’s results for Multistep Methods with the maximum order of accuracy were compared. Proven that the MultistepThriedderivative Methods are more accurate than the others. By using model problems have illustrated some results received here.

Plasmonic semi shells derived from simultaneous in situ gold growth and anisotropic acid etching of ZIF-8 for photothermal ablation of metastatic breast tumor

Open nanoshells such as nanobowls or nanocups collectively described as ‘semi shells’ have unique plasmonic properties due to their lack of symmetry. So far, their fabrication was based on multistep and laborious methods such as solid state sputter coating or selective deposition/etching using sacrificial templates. In this work, we report a rapid one step colloidal synthetic protocol for PEGylated semi-shell (SS) fabrication by simultaneous facet specific anisotropic chemical etching of rhombic dodecahedral ZIF-8 and heterogenous nucleation & growth of gold. The SS possesses a strong localized surface plasmon resonance in the near-infrared region, which is retained after surface passivation with polyethylene glycol and subsequent cryopreservation for extended shelf-life. Freshly reconstituted PEGylated SS was found to be safe & non-toxic in healthy C57BL/6 mice post intravenous administration. The PEGylated SS displayed significant photothermal efficiency of ~37% with 808 nm laser irradiation. Preclinical assessment of intra-tumoral photothermal efficacy indicated complete remission of primary breast tumor mass with insignificant metastasis to vital organs in 4T1 FL2 tumor bearing CD1 nude mice. Further, PEGylated SS mediated photothermal therapy also yielded morbidity free survivael of 75% for up to 90 days, indicating their potential to significantly improve outcomes in advanced breast tumors.

Paradigm on Levenberg–Marquardt neural algorithm analysis of heat conduction optimization for ternary hybrid nanofluid with entropy generation

AbstractThe significance of the present article is to enhance the thermal management and energy efficiency of complex engineering infrastructures such as energy storage systems, modern electric vehicles, thermal insulations, heavy‐duty machinery, and production units. This research aims to understand the intricate relationship between the thermal conductivity performance of ternary () hybrid nanomaterial and entropy generation to optimize material design and efficacy. A synergetic combination of three distinct nanomaterials silicon dioxide, ferric oxide, and titanium oxide with ethylene glycol and water in the ratio 3:2 as a base solvent is comprised of contributing unique thermophysical properties. To elucidate the impact of this hybrid composition on thermal conductivity, various factors are analyzed. The advanced computational technique of Artificial intelligent feed‐forward neural network (AIFFNN) is utilized. The problem governed the system of PDEs, which is transformed into ODEs by dimensionless similarity. Adams method provided the dataset which is filtered and embedded into Marquardt–Levenberg Algorithm (LMA). The study examines the role of nanomaterial constituents, morphology, and boundary conditions on thermal performance and entropy generation. Graphical analysis of velocity, temperature, and entropy is provided with respect to varying parameters, including surface absorption (λ), magnetic strength (Tesla M), radiation parameter (Rd), Brownian motion (Br), and Eckert number (Ec). The findings have practical significance for optimizing material design in engineering and industrial applications.

An extended study of two multistep higher order convergent methods for solving nonlinear equations

The local analysis of convergence for two competing methods of order seven or eight is developed to solve Banach space‐valued equations. Previous studies have used the eighth or ninth derivative of the operator involved, which do not appear on the methods, to show the convergence of these methods on the finite‐dimensional Euclidean space. In addition, no computable error distances or isolation of the solution results are provided in this study. These problems limit the applicability of this method to solving equations with operators that are at least nine times differentiable. In the current study, only conditions on the first derivative, appearing in these methods, are employed to show the convergence of these methods. Moreover, computable error bounds depend on the distance in the world as well as the isolation of the solution. Results are provided based on generalized continuity conditions on the first derivative. Furthermore, the more interesting semi‐local analysis of convergence not given before these methods is presented using a majorizing sequence. Finally, a great deal of impressive numerical results has been shown on real‐world problems.