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Four explicit numerical schemes are collected, which are stable and efficient for the diffusion equation. Using these diffusion solvers, several new methods are constructed for the nonlinear Huxley's equation. Then, based on many successive numerical case studies in one and two space dimensions, the least performing methods are gradually dropped out to keep only the best ones. During the tests, not only one but all the relevant time step sizes are considered, and for them, running-time measurements are performed. A major aspect is computational efficiency, which means that an acceptable solution is produced in the shortest possible time. Parameter sweeps are executed for the coefficient of the nonlinear term, the stiffness ratio, and the length of the examined time interval as well. We obtained that usually, the leapfrog–hopscotch method with Strang-type operator-splitting is the most efficient and reliable, but the method based on the Dufort–Frankel scheme can also be very efficient. [ABSTRACT FROM AUTHOR]

Interest in the use of container houses has been increasing in recent years because of their resistance to earthquakes and fires. The incorporation of recyclable materials into these houses will simultaneously reduce energy use and greenhouse gas emission rates. In this context, the thermal performance of an external multi-layer wall of a container house mostly made of recyclable materials is studied and compared to that of a normal wall. The current study proposes a completely new structure, where there are air gaps and plastic layers between the steel sheets to enhance thermal insulation. In these gaps, different gases including argon are tested to reduce the heat loss. Calculations are carried out for a steady-state case in the winter season using the student version of ANSYS 2023 R2 Academic software, and the heat loss is calculated for different materials and different thicknesses of the wall layers. Afterward, based on a life-cycle cost analysis, the optimum air gap materials, optimum thickness of plastic and air gap, and energy savings are determined for a period of 20 years. We found that the optimum number of plastic layers to minimize the heating load is 21, but this reduces to 11 when considering economic factors. Furthermore, if a reflective layer covers the plastic layer, the optimum is just one layer. For an insulation thickness of 2 cm, the maximum total life-cycle savings are 335.14 and 350.52 USD, respectively, and the minimum ones are 16.06 and 31.44 USD, respectively, for multi-layer walls with and without reflective layers compared to conventional walls. [ABSTRACT FROM AUTHOR]

The numerical solution to boundary differential problems is a crucial task in modern applied mathematics. Usually, implicit integration methods are applied to solve this class of problems due to their high numerical stability and convergence. The known shortcoming of implicit algorithms is high computational costs, which can become unacceptable in the case of numerous right-hand side function calls, which are typical when solving boundary problems via the shooting method. Meanwhile, recently semi-implicit numerical integrators have gained major interest from scholars, providing an efficient trade-off between computational costs, stability, and precision. However, the application of semi-implicit methods to solving boundary problems has not been investigated in detail. In this paper, we aim to fill this gap by constructing a semi-implicit boundary problem solver and comparing the performance of explicit, semi-implicit, semi-explicit, and implicit methods using a set of linear and nonlinear test boundary problems. The novel blinking solver concept is introduced to overcome the main shortcoming of the semi-implicit schemes, namely, the low convergence on exponential solutions. The numerical stability of the blinking semi-implicit solver is investigated and compared with existing methods by plotting the stability regions. The performance plots for investigated methods are obtained as a dependence between global truncation error and estimated computation time. The experimental results confirm the assumption that semi-implicit numerical methods can significantly outperform both explicit and implicit solvers while solving boundary problems, especially in the proposed blinking modification. The results of this study can be efficiently used to create software for solving boundary problems, including partial derivative equations. Constructing semi-implicit numerical methods of higher-accuracy orders is also of interest for further research. [ABSTRACT FROM AUTHOR]

In recent years, the need for high-performance computing solutions has increased due to the growing complexity of computational tasks. The use of parallel processing techniques has become essential to address this demand. In this study, an Open Computing Language (OpenCL)-based parallelization algorithm is implemented for the Constant Neighbors (CNe) and CNe with Predictor–Corrector (CpC) numerical methods, which are recently developed explicit and stable numerical algorithms to solve the heat conduction equation. The CPU time and error rate performance of these two methods are compared with the sequential implementation and Euler's explicit method. The results demonstrate that the parallel version's CPU time remains nearly constant under the examined circumstances, regardless of the number of spatial mesh points. This leads to a remarkable speed advantage over the sequential version for larger data point counts. Furthermore, the impact of the number of timesteps on the crossover point where the parallel version becomes faster than the sequential one is investigated. [ABSTRACT FROM AUTHOR]

The primary goal of this research was to empirically identify and validate the factors influencing student engagement in a learning environment where AI-based chat tools, such as ChatGPT or other large language models (LLMs), are intensively integrated into the curriculum and teaching–learning process. Traditional educational theories provide a robust framework for understanding diverse dimensions of student engagement, but the integration of AI-based tools offers new personalized learning experiences, immediate feedback, and resource accessibility that necessitate a contemporary exploration of these foundational concepts. Exploratory Factor Analysis (EFA) was utilized to uncover the underlying factor structure within a large set of variables, and Confirmatory Factor Analysis (CFA) was employed to verify the factor structure identified by EFA. Four new factors have been identified: "Academic Self-Efficacy and Preparedness", "Autonomy and Resource Utilization", "Interest and Engagement", and "Self-Regulation and Goal Setting." Based on these factors, a new engagement measuring scale has been developed to comprehensively assess student engagement in AI-enhanced learning environments. [ABSTRACT FROM AUTHOR]

Heat transfer processes in a photovoltaic (PV) silicon solar panel are simulated under standard circumstances. A model containing an intricate treatment of the incoming solar radiation, long‐wave radiation, conduction, convection, and electrical power output is developed in mathematical form. To solve the time‐dependent partial differential equation, recent explicit numerical methods are utilized, which are unconditionally stable for heat conduction problems. Since very realistic values are obtained for the temperature and the dependent electrical variables such as the power output, one can conclude that these methods are efficient. [ABSTRACT FROM AUTHOR]

Canary grass (Phalaris canariensis L.) is a versatile crop with global significance; it is primarily cultivated for its small elliptical seeds, which are used as bird feed and for human consumption. This crop is adapted to various climates and soils, so it can be grown successfully in Hungary. However, challenges such as weed control, climate change impacts, and soil factors require strategic management for sustained success in canary grass cultivation. Our study investigated the impact of management and environmental (as seasonal and soil) factors on pre-harvest weed vegetation in canary grass fields in Southeast Hungary between 2017 and 2020. In addition to showing the weed vegetation of the canary grass, the aim of our work was to promote more effective weed management of canary grass by revealing correlations between soil, seasonality, and management variables, influencing weed diversity and coverage. Using the analysis of covariance (ANCOVA) and correlation tests, we tested significant variables, providing insights into the complex interactions affecting weed composition. A redundancy analysis (RDA) further unveiled the relationships between explanatory variables and weed species' composition. The findings offer valuable information for effective weed management strategies in canary grass cultivation. Our comprehensive study on canary grass fields in Southeast Hungary sheds light on significant factors influencing weed composition and abundance. The average weed coverage was 10.8%, with summer annuals and creeping perennials being the most prevalent life forms. Echinochloa crus-galli, Cirsium arvense, Xanthium italicum, and Setaria viridis were among the dominant species. ANCOVAs revealed the impact of soil, management, and seasonal factors on weed cover, species richness, diversity, and yield levels. Soil properties like texture, pH, and nitrogen content showed varying effects on weed parameters. The vintage effect, tillage systems, and farming practices also played crucial roles. The redundancy analysis highlighted the influence of the year, soil sulfur content, and winter preceding crops on weed composition. In conclusion, the herbaceous vegetation in the studied area is dominated by summer germinating and creeping perennial species. Despite slight differences in average coverage and occurrence, a well-defined set of significant species is evident. Multicollinearity among variables suggests limitations to further increase the number of variables that can be included in the analysis. The ANCOVAs showed that the soil, seasonal, and farming variables significantly influence overall weed vegetation and crop yield, with a lesser impact on species richness and diversity. The reduced RDA model highlights the strong influence of the year on species' composition, emphasizing the inherent factors during canary grass cultivation that are challenging to modify through farming practices. [ABSTRACT FROM AUTHOR]

Pea is a widely cultivated leguminous plant which also contributes to soil enrichment through nitrogen fixation and benefits crop rotations. However, large weed populations are a challenge for pea production, requiring effective management strategies. It is essential to highlight the influence of soil parameters, factors affecting the environment, and management practices on weed populations to develop effective weed control and maximize pea yield and ease of harvesting. In our study, a total of 31 pea fields were surveyed prior to harvest to determine the coverage of each weed species, with the aim of identifying the typical weeds in the study area. In addition, environmental, soil, and management factors were recorded for each field. Based on our hypotheses, these factors influence the weed composition, and these effects can be described by the dominance of weed species. In our study, summer annuals and geophytic perennials were common, with Echinochloa crus-galli and Convolvulus arvensis being most dominant. The analysis revealed that the year of data record, soil type, and farming system most significantly influenced weed composition. Weed species were observed to have varying responses to soil texture, salt concentration, and phosphorus content. The survey period, geographical factors, farming system, and tillage practices also played a role in determining weed flora. The findings suggest strong correlations between soil parameters and weed composition, highlighting the importance of soil management in weed control. The year of data collection had the greatest influence on weed infestation. Soil-related variables, such as soil type, also played a significant role. Farming systems had a smaller effect on weed composition. Comparing our results with previous country level weed surveys in Hungary, our results identified some unique characteristics in the weed flora of South-East Hungary. [ABSTRACT FROM AUTHOR]

We systematically test families of explicit adaptive step size controllers for solving the diffusion or heat equation. After discretizing the space variables as in the conventional method of lines, we are left with a system of ordinary differential equations (ODEs). Different methods for estimating the local error and techniques for changing the step size when solving a system of ODEs were suggested previously by researchers. In this paper, those local error estimators and techniques are used to generate different types of adaptive step size controllers. Those controllers are applied to a system of ODEs resulting from discretizing diffusion equations. The performances of the controllers were compared in the cases of three different experiments. The first and the second system are heat conduction in homogeneous and inhomogeneous media, while the third one contains a moving heat source that can correspond to a welding process. [ABSTRACT FROM AUTHOR]

We utilize the travelling-wave Ansatz to obtain novel analytical solutions to the linear diffusion–reaction equation. The reaction term is a function of time and space simultaneously, firstly in a Lorentzian form and secondly in a cosine travelling-wave form. The new solutions contain the Heun functions in the first case and the Mathieu functions for the second case, and therefore are highly nontrivial. We use these solutions to test some non-conventional explicit and stable numerical methods against the standard explicit and implicit methods, where in the latter case the algebraic equation system is solved by the preconditioned conjugate gradient and the GMRES solvers. After this verification, we also calculate the transient temperature of a 2D surface subjected to the cooling effect of the wind, which is a function of space and time again. We obtain that the explicit stable methods can reach the accuracy of the implicit solvers in orders of magnitude shorter time. [ABSTRACT FROM AUTHOR]