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This paper deals with the numerical investigation of a singularly perturbed parabolic differential-difference equation with a time lag. The proposed method comprises the θ method (θ=1) and the non-standard finite difference methods for temporal and spatial variable discretization, respectively. Besides, the Richardson extrapolation technique is employed to boost the accuracy and order of convergence of the scheme. The applicability of the proposed approach is confirmed through some numerical examples. Furthermore, we have improved the convergence from almost first to almost second order.

Background: Pain management is a crucial component of patient care that promotes relaxation, lowers complications, improves quality of life, and shortens hospital stays. Several studies assessed the nurses' pain management practices in Ethiopia. However, the findings of these studies are highly variable and inconsistent. Therefore, the study aims to determine the overall prevalence of pain management practice and associated factors among nurses working in Ethiopia. Method: The study included all observational quantitative research articles conducted among nurses in Ethiopia. We used Google Scholar, PubMed, Cochrane Library, and Scopus searching databases. The Newcastle—Ottawa Scale was used to check the study quality. Then I2 statistics and Cochran's Q test were used to evaluate heterogeneity. The Funnel, Egger's test, and non-parametric trim and fill effect tests were used to check publication bias by using a random effect model. Finally, we conducted subgroup analysis and sensitivity tests to evaluate statistical heterogeneity and the presence or absence of any influential study. Result: In the final analysis, we included eighteen studies, and 4,213 nurses participated. The overall pooled prevalence of nurses with good pain management practice was 43.79% (95% CI: 38.52, 49.06%). In-service training AOR; 95% CI 3.21 (1.87, 4.54), good knowledge AOR; 95% CI 2.44 (1.78, 3.09), positive attitudes AOR; 95% CI 2.84 (1.24, 4.44), and pain management guidelines in health facilities AOR; 95% CI 3.46 (1.48, 5.44) were the significant associated factors with pain management practice among nurses in Ethiopia. Conclusion: This study found that over half of Ethiopian nurses had poor pain management practices. Knowledge, attitude, training, and pain management guidelines in health facilities were significant factors. Therefore, health managers and stakeholders should prioritize pain management awareness, attitudes, availability of guidelines, and in-service training to improve patient care and outcomes. [ABSTRACT FROM AUTHOR]

This study explored the status of primary and middle school physical education (PE) teachers' professional knowledge competence (PKC) in the Amhara Region, in Ethiopia. For this, a quantitative research approach was employed and data were collected from 382 randomly selected PE teachers and analysed quantitatively. Findings revealed that the overall PKC of PE was low. Statistically, a significant difference was observed among PE teachers in their content knowledge (CK), pedagogical knowledge (PK), pedagogical content knowledge (PCK), and PKC. Female PE teachers, novice PE teachers, and rural PE teachers were less competent in their CK, PK, and PCK. Besides, unlike in their PK, degree-holder PE teachers have better CK, PCK, and PKC than diploma holders. Accordingly, due care and special intervention need to be given by the education actors in the recruitment, training, and deployment of PE teachers in Ethiopia. [ABSTRACT FROM AUTHOR]