Starting procedures for IMEX general linear methods to solve Stiff-Nonstiff differential equations

A Parameter-Dependent Second-Derivative General Linear Method with Nearly Runge–Kutta Stability

Efficient numerical methods based on general linear methods for Volterra integral equations

Background: Soybean breeding program face challenges due to genotype-by-environment interaction (GEI), where genotypes exhibit varying performance across different environments, complicating the identification of stable, high-yield cultivars. This study aimed to elucidate GEI’s impact on soybean yield and identify genotypes with superior adaptation and yield stability across diverse environments. Methods: Fifty genotypes were evaluated over three years in a randomized block design with three replications per environment, assessing yield components and other agronomic traits. Stability performance was analyzed using general linear methods, GGE biplot, AMMI analysis and ASV rank analysis. Result: The GGE biplot explained 75.10% of the total variation (PC1: 30.93%, PC2: 44.8%), while the AMMI model’s first two interaction principal component axes (IPCA1: 59.3%, IPCA2: 40.7%) explained the GEI variation. AMMI analysis identified G26 (JS 22-88) and G39 (JS 22-101) as the most stable, high-performing genotypes, whereas GGE biplot analysis identified G9 (JS 22-71).

Financing SMEs is considered one of the most important tools in middle east. To support SMEs, and sustain their business, the existence of financial solutions that comply with the Islamic rules will provide more alternatives for SMEs to finance their short-term obligations represented in profit and loss sharing tools (Musharakah and Modaraba). This study is based on using partnership as an approach to finance SMEs. The study was conducted in Kingdom of Bahrain. Recently, many financial institutions started to adopt many Islamic financial tools. The purpose of this study is exploring how the partnership is different from the traditional financial solutions and the impact of it on nonbanking financial institutions and on the financial services. The study was conducted through a five-points Likert scale questionnaire as the research instrument. The respondents of the study are the employees in nonbanking financial service providers and SMEs in Bahrain. The statistical techniques used in the study are Correlation Analysis, General Linear Model Structural Equation Methods and Path Analysis. The results showed a strong positive and significant correlation between partnership, non-banking financial institutions, financial services and SMEs. The study provides suggestions and recommendations for SMEs in Kingdom of Bahrain to have more alternatives to finance their operations.

Numerical methods for solving ordinary differential equations (ODEs) are essential in modeling dynamical systems across science and engineering. While specialized methods exist for first-order and second-order ODEs, developing a unified approach that efficiently handles both classes remain an active area of research. In this paper, we present a novel two-step hybrid block method based on the backward differentiation formula (BDF), capable of approximating solutions for both first- and second-order ODEs without requiring separate derivations. The method is constructed using interpolation and collocation techniques, and its numerical analysis confirms consistency, zero-stability, and convergence. Furthermore, stability analysis via the general linear method demonstrates that the scheme is A-stable, making it suitable for stiff systems. Numerical experiments including applications to the SIR epidemic model, Riccati differential equations, nonlinear stiff chemical systems, and second-order nonlinear ODEs—validate the method’s accuracy and computational efficiency. Comparative results with existing methods in the literature highlight its superior performance in terms of error reduction and stability. This work contributes a versatile, high-precision tool for ODE solutions, bridging gaps in the adaptability of traditional BDF-based approaches.

Ethiopia's genetic enhancement efforts have included directly importing exotic cattle from other countries or introducing genes from an external source via artificial insemination (AI) to enhance the breed composition of local cattle. The study aimed to evaluate the status of artificial insemination and identify its constraints in the selected districts of East Arsi Zone, Oromia regional state. The data were collected from 301 farmers and 9 AI technicians (AIT) using semi-structured questionnaires. Five-year secondary data were used from the annual summary of the casebook to evaluate AI status. Data on AI status, satisfaction, breeding method, controlled mating and AI delivery were analyzed using Statistical Analysis Systems (SAS) chi-square procedures. Secondary data were analyzed using General Linear Model SAS methods. The ranking coefficient was analyzed using the R software Plackett–Luce model procedure. The study found that 43.52% of participants were dissatisfied with AI services, while 56.48% were satisfied. Furthermore, 72.43% of respondents indicated an increase in AI services, whereas 13.62% reported a decrease and 13.95% no change. The respondents' satisfaction with AI and AI status differed (P<0.05) among districts, but no difference (P>0.05) between the production systems. The secondary data revealed a gradual increase in AI delivery from 2018 to 2022. The average AI delivery was 2281.5±275.6 per year. While AI services did not differ (P > 0.05) across districts, there was a significant (P< 0.05) variation over time. About 55.48% of the districts' dairy producers used AI for breeding. Most respondents (61.79%) received AI from government administrations, while 36.21% received from government and private and only 1.99% obtained it from private suppliers. Breeding methods varied significantly across production systems (P<0.0001), but controlled mating and AI provision were non-significant. The farmers preferred neighbor bulls with estimated coefficients of 2.24 followed by their bulls (1.05) for breeding purposes. The respondents indicated that conception failure (0.72) and poor conception rates (0.56) were the biggest challenges for AI in the study areas. Transportation (2.89) was the main constraint in delivering AI services identified by AITs. Despite these challenges, there has been an increase in the use of AI in study areas over the past five years. Because AI is the only accessible technology for increasing dairy cow performance in the country, it is vital to address these challenges to increase AI utilization in the study regions. Focusing on semen quality is necessary to achieve a high conception rate per service. Supporting commercial AI businesses could improve farmers' access to services. Key words: artificial insemination, breeding method, controlled mating, satisfaction, status

Error estimates of general linear and spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian

Variable stepsize general linear methods for ODEs

A second order implicit-explicit general linear method based on continuous interpolants

Several studies have reported associations between substance use and effort-related decision making, or the degree to which effort expenditure impacts the choice between lower and higher value rewards. However, previous research has not explored effort-related decision making in populations with severe substance use disorder. Investigate the association between effort-related decision-making and substance use disorder severity. Adults with substance use disorders (n = 106) enrolled in intensive outpatient treatment completed clinician administered diagnostic interviews and the effort expenditure for rewards task (EEfRT). General linear mixed methods tested the interactive effect of substance use disorder severity and trial-level probability and value on the likelihood of selecting a high-effort choice. There was a significant interaction between SUD severity and both reward value and reward probability on high-effort choice. The strength of the association between both reward value and probability on high-effort choice significantly increased with SUD severity. These results support theories of reward sensitivity and behavioral economics and highlight an emerging risk factor that may serve as a useful target for treatment.

Acupuncture on the acupuncture point GV20 has been considered effective for managing psychoneurological disorders since ancient times, and GV20 is now regularly used to treat stress-related diseases (SRDs), including psychoneurological disorders. Although reports indicating that acupuncture stimulation of GV20 alone regulates cerebral blood flow (CBF) in brain regions associated with SRDs have been scattered, from the perspective of the need for earlier action, the effects on subjective stress as self-reported in the stress state of healthy individuals and CBF changes in related prefrontal cortex (PFC) subregions, which is based as underlying mechanism, remain unclear. Therefore, there is a need to explore effective methods for analyzing such effects. Multiple consecutive mental arithmetic tasks were performed to induce sufficient stress in healthy university students. Real acupuncture or sham acupuncture was performed on GV20, and subjective stress and CBF changes in PFC subregions were observed before and after acupuncture using functional near-infrared spectroscopy, which were analyzed based on the general linear model method and correlation analysis. Subjective stress was suppressed and recovered significantly faster in the true acupuncture group than in the sham acupuncture group. Furthermore, significant negative correlations were found between subjective stress and CBF in several PFC subregions during and after the tasks, with more correlated regions on the left side than on the right side of the PFC. Among them, the CBF of the left ventrolateral PFC (vl-PFC) was suggested to be maintained in the true acupuncture group under repeated tasks load, which was inferred to be correlated with delayed decreases in subjective stress after acupuncture. This pilot study showed that fNIRS is feasible for assessing delayed PFC inhibition in acute stress by acupuncture on GV20. Acupuncture treatment on GV20 resulted in early suppression of subjective stress and early recovery. The neuroscientific rationale for this finding may lie in its effect on maintaining CBF in the left vl-PFC related to delayed inhibition of subjective stress, and would make it reasonable to apply acupuncture to GV20 in healthy individuals. Larger studies are needed to corroborate these findings and obtain reliable conclusions.

Solving nonlinear neutral delay integro-differential equations via general linear methods

Abstract. Leptin (LEP), alternatively recognized as the obesity gene, influences food consumption, energy balance, and lipid metabolism. Additionally, it plays a crucial role in energy metabolism, and variations in the LEP gene have been studied extensively among various livestock species. These investigations have unveiled correlations with traits such as meat quality, milk yield and composition, and growth characteristics. Nevertheless, the existing knowledge regarding its correlation with growth and reproductive traits in goats is comparatively limited, particularly when juxtaposed with studies of cattle. Hence, the objective of the current study was to investigate the relationship between polymorphisms in the intron 2 (Sau3AI) and exon 2 (HinfI) regions of the LEP gene and growth and reproductive traits in Saanen goats. The study comprised 185 Saanen goats in total. The PCR-RFLP (polymerase chain reaction restriction fragment length polymorphism) technique was employed to genotype these polymorphisms. Population genetic analysis included the number of effective alleles, heterozygosity, polymorphism information content, and compatibility with the Hardy–Weinberg equilibrium. The general linear model procedure's least-squares methods were used for the statistical analysis. The SNP (single-nucleotide polymorphism) located in exon 2 (LEP-HinfI) was monomorphic. Remarkably, the SNP located in intron 2 (LEP-Sau3AI) was associated with birth weight (p<0.05) and average daily weight gain (p<0.05). In this context, the AA genotype demonstrated higher birth weight and daily live weight gain means compared to other genotypes. No significant differences were observed in litter size, total weight gain, or morphometric measurements. The caprine LEP-Sau3AI polymorphism situated within intron 2 proved influential in traits critical for the profitability and sustainability of goat breeding. The findings of this study provide novel and valuable information for future research on the LEP gene in goats.

In this paper, we construct explicit second derivative general linear methods (SGLMs) with quadratic stability and a large region of absolute stability for the numerical solution of non-stiff ODEs. The methods are constructed in two different cases: SGLMs with p = q = r = s and SGLMs with p = q and r = s = 2 in which p, q, r and s are respectively the order, stage order, the number of external stages and the number of internal stages. Examples of the methods up to order five are given. The efficiency of the constructed methods is illustrated by applying them to some well-known non-stiff problems and comparing the obtained results with those of general linear methods of the same order and stage order.

Genotype × environment interaction (GEI) poses a critical challenge to plant breeders by complicating the identification of stable variety (ies) for performance across diverse environments. GGE biplot and AMMI analyses have been identified as the most effective and appropriate statistical techniques for identifying stable and high-performing genotypes across diverse environments. The objective of this study was to identify widely adapted and high-yielding soybean genotypes from Multi-Locational Trials (MLTs) using GGE and AMMI biplot analyses. Fifteen IITA-bred elite soybean lines and three standard checks were evaluated for stability of performance in a 3 × 6 alpha lattice design with three replications across seven locations in Nigeria. Significant (p < 0.001) differences were detected among genotypes, environments, and GEI for grain yield, which ranged between 979.8 kg ha−1 and 3645 kg ha−1 with a mean of 2324 kg ha−1. To assess the stability of genotypes, analyses were conducted using the general linear method, GGE, and the Additive Main Effect and Multiplicative Interaction (AMMI) approach, as well as WAAS and ASV rank indices. In the GGE biplot model, the first two principal components accounted for 67.4 % of the total variation, while in the AMMI model, the first two Interaction Principal Component Axes (IPCA1 and IPCA2) explained 73.20 % and 11.40 % of the variation attributed to genotype by environment interaction, respectively. GGE biplot identified G10 and G16 as the most stable and productive genotypes, while WAASB index revealed G16, G10, G9, G4 and G2 as the most adaptive, stable and productive genotypes across locations, and ASV identified G9, G13, G4, G14 and G10 as the most stable and productive.Consequently, genotypes G2, G4, G9, G10 and G16 displayed outstanding and stable grain yield performance across the test locations and are, therefore, recommended for release as new soybean varieties suitable for cultivation in the respective mega environment where they performed best. More importantly, the two genotypes are recommended for recycling as sources of high-yield and yield stability genes, and as parental lines for high-yield and stable performance for future breeding and genomic selection.

The association of Healthy Eating Index 2020 (HEI-2020), especially its components with systemic inflammatory biomarkers, has not been examined. The aim of this study was to investigate the relationship between HEI-2020 and its components with systemic inflammatory biomarkers, and to provide a dietary pattern suggestion to combat systemic inflammation. Participants aged 20 years and older with complete information on two reliable dietary recalls, blood cell counts and demographic characteristics, were recruited from six NHANES cycles from 2007 to 2018. Weighted general linear methods showed that HEI-2020 was negatively associated with systemic immune-inflammation index (SII) and systemic inflammation response index (SIRI). Weighted quantile regression (WQS) models and quantile g-computation (QGC) models supported the negative association between the mixed components and systemic inflammation. High intakes of whole fruits, whole grains, greens and beans, and seafood and plant proteins, along with a low intake of added sugars, were associated with reduced systemic inflammation. In contrast, the scores of sodium, dairy, total protein, and refined grains showed no significant effect. Briefly, our study provides an anti-inflammatory dietary pattern suggestion based on the 13 components of HEI-2020 and Dietary Guidelines for Americans.

Jacobian-free explicit multiderivative general linear methods for hyperbolic conservation laws

As a cigarette butt falls onto the forest surface fuel, it first smolders the fuel, then ignites into flames, and spreads as forest fire under certain conditions. In this study, the needles under a typical stand of P. massoniana were used as the research object. Needle beds with different moisture content and packing ratios were constructed indoors. Cigarette butt-ignition experiments were conducted under different wind velocities, and 30 experiment cycles were conducted under different conditions. There was a total of 5 (packing ratio) × 4 (moisture content) × 6 (wind velocity) = 120 sets of conditions, and a total of 3600 ignition experiments were conducted. The results showed that (1) the total ignition probability of the cigarette butts was 2.36%, which only occurred when the fuelbed moisture content was &lt;10% and the wind velocity was &gt;1 m/s. The ignition time of cigarette butts ranged from 2.73 to 7.25 min. (2) The fuelbed moisture content and wind velocity significantly influenced the ignition probability and time. With an increase in moisture content, the ignition probability of cigarette butts decreased, while the time required for ignition showed an increasing trend. Wind velocity had a dual effect on ignition. The ignition effect was optimal at a wind velocity of 4 m/s. With an increase in wind velocity, the ignition probability first increased and then decreased, and the ignition time first decreased and then increased. (3) The packing ratio had no significant effect on the ignition probability; however, the ignition time significantly decreased as the packing ratio increased. (4) The logistic regression method (LRM), general linear method (GLM), and nonlinear regression method (NLM) were used to establish a prediction model of ignition probability. The prediction effect of GLM was the worst, followed by LRM, and the NLM had the best prediction effect. The GLM was selected to establish the ignition time model, and the error was also within the allowance range. This study elucidated the underlying mechanism of factors affecting cigarette butt-based fuel ignition. In addition, the established prediction model provides a reference for human-caused forest fires and is highly significant for forest fire prevention.

Recently, a stability theory has been developed to study the linear stability of modified Patankar–Runge–Kutta (MPRK) schemes. This stability theory provides sufficient conditions for a fixed point of an MPRK scheme to be stable as well as for the convergence of an MPRK scheme towards the steady state of the corresponding initial value problem, whereas the main assumption is that the initial value is sufficiently close to the steady state. Initially, numerical experiments in several publications indicated that these linear stability properties are not only local but even global, as is the case for general linear methods. Recently, however, it was discovered that the linear stability of the MPDeC(8) scheme is indeed only local in nature. Our conjecture is that this is a result of negative Runge–Kutta (RK) parameters of MPDeC(8) and that linear stability is indeed global if the RK parameters are nonnegative. To support this conjecture, we examine the family of MPRK22(α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{\\alpha }$$\\end{document}) methods with negative RK parameters and show that even among these methods there are methods for which the stability properties are only local. However, this local linear stability is not observed for MPRK22(α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}) schemes with nonnegative Runge–Kutta parameters. In particular, it is shown that MPRK22(α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}) schemes with 0<α<0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0<\\alpha <0.5$$\\end{document} or -0.5<α<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-0.5<\\alpha <0$$\\end{document} are only stable if the time step size is sufficiently small. But schemes with α≤-0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\le -0.5$$\\end{document} are stable and converge towards the steady state of the initial value problems for all time step sizes, at least for the test problem under consideration. Furthermore, it is shown that for some of the latter systems, the initial values must actually be close enough to the steady state to guarantee this result.