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This research explores the use of iterative methods in conjunction with the Finite Difference Method (FDM) for solving partial differential equations (PDE). The central challenge addressed is the computational inefficiency and slow convergence that often arise when utilizing traditional numerical methods, particularly in large-scale systems. The study aims to develop a more efficient iterative approach to solve PDEs by minimizing computational time while ensuring the stability of the obtained solutions. The primary methods proposed include iterative solvers such as Gauss-Seidel and Successive Over-Relaxation (SOR), which are applied to numerical solutions derived from FDM. The research demonstrates that iterative methods, especially SOR, achieve faster convergence with fewer iterations compared to conventional methods like the Finite Element Method (FEM), which tends to be slower and more resource-intensive for large-scale problems. The study highlights the advantages of iterative solvers in efficiently handling large, sparse linear systems and reducing computational costs. In addition, it shows that these methods are capable of providing stable solutions, thereby maintaining accuracy with significantly lower computational effort. The results suggest that iterative methods, when applied in combination with FDM, offer a practical and scalable solution for solving complex PDEs. These methods are especially beneficial in engineering and theoretical physics applications where large-scale simulations are prevalent. The study concludes with recommendations for future research, which should focus on further optimizing solver parameters, exploring hybrid approaches, and extending the methods to more complex PDEs with non-linearities or irregular geometries. By doing so, these techniques could contribute to even more efficient and practical solutions for real-world applications.

Combinatorial optimization is a fundamental area in operations research and computer science, focusing on identifying optimal solutions from a finite set of possibilities. This study explores the integration of branch and bound methods with heuristic algorithms to address optimization problems in graph theory and discrete mathematics. Python was employed for algorithm implementation due to its flexibility and comprehensive computational libraries, enabling efficient data analysis and visualization. Several benchmark problems were examined, including the Traveling Salesman Problem (TSP), Minimum Spanning Tree (MST), and Graph Coloring. Simulations were conducted using datasets of varying sizes (small, medium, and large) to evaluate performance across different scales. The results demonstrate that the hybrid approach achieves a balance between solution quality and computational efficiency, outperforming brute-force methods in terms of speed while maintaining near-optimal accuracy. Tabulated results and graphical comparisons highlight the reduction in computation time and improved scalability of the proposed method. The findings suggest that combining systematic search strategies with heuristics offers a practical and effective framework for solving complex combinatorial optimization problems. Recommendations for future research include testing scalability with larger datasets, incorporating advanced metaheuristics, and applying the approach to real-world domains such as logistics and network design.

The revised Bloom's Taxonomy is a framework of thinking that is widely used in education to design learning objectives, assessments, and curricula. The revised taxonomy by Anderson and Krathwohl changes the classification from nouns to operational verbs, starting from low to high cognitive levels: remember, understand, apply, analyze, evaluate, and create. This study aims to analyze the application of creative ability (C6) in Islamic Jurisprudence learning at MI Nurul Qodim, especially in the context of implementing the Revised Bloom's Taxonomy. This study uses a descriptive qualitative approach with observation, interviews, and documentation techniques. The results of the study indicate that students' creative abilities in Islamic Jurisprudence learning have not yet developed optimally. This is due to the learning method that still focuses on basic concepts in textbooks and the limited experience of students in solving contextual problems. Lower-grade students are still dominant in playing, while upper-grade students begin to show their ability to argue and solve simple problems. Therefore, a more innovative and contextual learning approach is needed to hone high-level thinking skills, especially in the realm of creating (C6).  

The purpose of this study was to determine the care skills of nurses. In carrying out their profession, care is required to improve skills which is a process that leads to professionalism. The process begins with the perception of nurses in seeing conditions and solving problems, one of which is carrying out the application of nursing care to clients. The application of nursing care provided by nurses cannot be separated from spiritual aspects which are an integral part of the nurse's interaction with clients. Nurses together with special spiritual officers in the hospital try to help meet the spiritual needs of clients as part of the client's overall needs, among others by facilitating the fulfillment of these client needs, even though nurses and clients do not have the same beliefs and religions. In the application of spiritual nursing care is influenced by several factors, namely intellectual skills where the nurse's intellect will be very influential in the application of care. With data collection methods, namely observation, documentation and questionnaires. The population and sample are Samples In this study, the sampling technique used was purposive sampling, namely the sample taken was 50 nurses who served in four rooms of the Inpatient Hospital Labuang Baji Makassar.

Education and health care for diabetes mellitus in Environment Objective: This implementation is to increase knowledge and health care about diabetes mellitus in Environment XIX, Tanjung Mulia Hilir Village, Medan Deli District. Health promotion for diabetes mellitus (DM) focuses on empowering individuals and communities to make sustainable lifestyle changes that prevent or delay the onset of type 2 diabetes and effectively manage existing diabetes to minimize complications. This method involves a multifaceted approach that includes: 1). Prevention, namely increasing awareness by educating the public about diabetes risk factors (such as obesity, lack of physical activity, unhealthy eating patterns, family history) and promoting healthy lifestyle choices. Encourage regular screening for early diagnosis, especially for those with risk factors. Promote healthy eating habits, regular physical activity, and maintaining a healthy weight.  Expected Outcome: increasing public awareness of diabetes risk factors (such as obesity, lack of physical activity, unhealthy diet, family history) and promoting healthy lifestyle choices. As well as the existence of guidelines for healthy eating and physical activity. Mechanisms for solving problems and overcoming them.

Employee Performance Assessment Decision Support System Using SAW Method at PT Hasta Bersama Prima Jaya Based on Java. The purpose of this study is to develop an existing employee performance assessment decision support system to facilitate data collection and employee performance assessment process. The research methodology used in the data processing system is the literature study method, namely data collection carried out by taking data from various books in the library, journals and other books that can be used as a basis for analyzing problems that can be discussed in the study, as well as the field study method, namely by conducting direct observations such as interviews and observations. The algorithm in solving the problem used is Simple Additive Weighting. The results of this study are the existence of an application device made with the Java programming language and data storage using a MySQL database so that the process of data collection and employee performance assessment at PT Hasta Bersama Prima Jaya becomes more effective, efficient and practical.

Mathematics is a universal science that underlies the development of modern technology, plays an important role in various scientific disciplines, and human thinking abilities. The view that mathematics is a science that trains thinking. The Creative Problem Solving learning model is a learning model that focuses on teaching and Problem Solving skills. Digital teaching materials are use digital devices, such as computers, smartphones. The aim of this research is to see the validity, practicality and effectiveness of the e-module being developed. This teaching material development model uses the ADDIE model. This research was carried out at SMP Negeri 21 Medan which is located on Jl. Rampe Raya flower. The time for the panel research is the even semester of the 2023/2024 academic year. The subjects of this research were class VII students at SMP Negeri 21 Medan. Meanwhile, the object of this research is learning media in the form of e-modules using flipbooks based on Creative Problem Solving. The e-module was declared very valid with a score of 3.56 and was categorized as very feasible. The e-module was declared practical with a percentage of 92.67% and was categorized as very practical. The e-module was declared effective by achieving Problem Solving indicators in indicators 1, 2, 3 and 4 with 65% of students completing the learning. The achievement of classical student indicators has met 65% of students who took part in learning with a score of 75. And there was a significant increase in indicators 1, 2, 3, and 4.

This research investigates ship maintenance management practices among senior students in shipping engineering during their internships at a vocational school in Jakarta. The study explores the challenges faced, strategies employed, and lessons learned in managing maintenance tasks onboard ships. Seven participants were interviewed, highlighting technical malfunctions, resource limitations, time constraints, environmental factors, and communication barriers as primary challenges. Participants utilized preventive maintenance, cross-training, task prioritization, collaborative problem-solving, and digital tools to enhance operational efficiency. Lessons underscored the importance of preparation, teamwork, adaptability, continuous learning, and communication skills in navigating maritime maintenance complexities. The findings emphasize the role of proactive maintenance strategies and technological integration in optimizing sustainability and operational reliability within the maritime industry. Integrating practical training into educational curricula and embracing digital innovations are recommended for preparing future professionals. Future research could explore larger sample sizes and quantitative methodologies to validate findings and quantify the impact of maintenance practices. This study contributes to enhancing vocational education in maritime sciences and informs industry practices for advancing ship maintenance management globally.

This research is classroom action research, this research was conducted in class X6 of SMA Negeri 8 Denpasar. Based on the researcher's initial observations at SMA Negeri 8 Denpasar, several problems were found that affected student learning outcomes, especially physical fitness material. As an alternative to solving existing problems, researchers provide a solution in the form of putting into practice a cooperative learning model of the Student Teams Achievement Division (STAD) type with the aim of improving the physical fitness results of class X6 students. This investigation is classroom action research, this investigation was carried out in class X6 of SMA Negeri 8 Denpasar. A population of 45 people was used, and the entirety was used as a sample. The cycle in this research was carried out until it reached completion in accordance with the KKTP that had been determined at SMA Negeri 8 Denpasar, namely 75. After implementing the STAD type cooperative learning model, the average final score of students increased beyond the KKTP that had been determined.  It can be concluded that the application of the STAD type cooperative learning model can improve physical fitness learning outcomes in class X6 students at SMA Negeri 8 Denpasar.

This research discusses the importance of building an entrepreneurial spirit among teenagers, especially by utilizing Rumah Honai creations as an innovative means. Entrepreneurship is seen as a key skill for the younger generation in facing future challenges and contributing to economic growth. Asset-Based Community Development Method (ABCD) is used to identify and utilize community potential and assets in developing empowerment programs. The discussion focuses on two main aspects: building an entrepreneurial spirit and combining innovation, culture and entrepreneurship through Rumah Honai. The development of an entrepreneurial spirit is emphasized as a continuous process that requires commitment, continuous learning and the ability to adapt. The Honai House, as a symbol of Papuan cultural heritage, was introduced as a creative tool to instill entrepreneurial values ​​such as creativity, risk taking and problem solving. This research shows that involving teenagers in the creation of Honai Houses can develop practical business skills, increase cultural awareness, and promote social responsibility. This approach not only builds a strong entrepreneurial foundation but also promotes cultural heritage preservation and sustainable social development. In conclusion, the integration of entrepreneurship with cultural elements such as Rumah Honai offers a holistic approach in preparing the younger generation to face future challenges, while maintaining their cultural identity.

This research aims to improve students' mathematical problem solving abilities by using a learning model Think Aloud Pair Problem Solving (TAPPS) with the help of animated videos. The research was conducted at SMA Negeri 1 Sumbul involving 36 class X-G students as research subjects. The type of research used is classroom action research (PTK) with steps, namely, providing an initial test to measure students' mathematical problem solving abilities before taking action, identifying problems in the classroom, planning action, implementing action, namely applying the TAPPS learning model (Think Aloud Pair Problem Solving) With the help of animated videos as a medium for conveying summaries of learning material, observation, giving post tests, data analysis and data reflection.  The research was carried out in 2 cycles where each cycle included two meetings, while observation activities were carried out simultaneously with the implementation of actions with the aim of observing the activities of researchers and students during learning activities. The research results showed that after the first cycle of research was carried out, the average student score from the pretest results to the first cycle posttest results increased from 52.56 to 72.94 with the average observation of student and researcher activities being 2.38 and 2.38. In the second cycle, students' mathematical problem solving abilities increased based on the average student score on posttest II, namely 84.62, the results of observations in the second cycle also improved better to 3.23 for student activities and 3.44 for researchers' ability to manage class, apart from that 34 out of 36 students (94%) obtained scores above the KKM (70). These results show that students' mathematical problem solving abilities increased after implementing the TAPPS learning model (Think Aloud Pair Problem Solving) Assisted by animated videos.

This research aims to determine the influence of learning styles on students' mathematical problem solving abilities. This research was carried out at MAS Al-Falah Klender. The method used is an ex post facto survey method with random sampling technique. The population in this study were class Data were collected using tests and analyzed by one way ANOVA. The results of this research show that 1) students' learning styles influence their mathematical problem solving abilities. 2) there is no significant difference between students' mathematical problem solving abilities with visual and auditory learning styles. 3) there is a significant difference between the mathematical problem solving abilities of students with kinesthetic and visual learning styles. 4) there is a significant difference between the mathematical problem solving abilities of students with kinesthetic and auditory learning styles.

This research is based on the low numeracy literacy skills of students, which are due to their unfamiliarity with solving numeracy literacy problems and the limited availability of such problems, making it difficult for teachers to provide numeracy literacy problems to students. Therefore, it is necessary to develop math problems that can measure students' numeracy literacy skills. The method applied in this research is Research and Development with the ADDIE model (Analysis, Design, Development, Implementation, Evaluation) without implementing the fourth and fifth stages. The development process starts from the analysis stage, which includes curriculum analysis, needs analysis, and material and problem analysis. After that, in the design stage, a product prototype is designed, and in the development stage, the product is consulted with three experts as validators. Next, the product is tested on students to determine its validity and reliability. The results show that all problems have a validity coefficient greater than , which means that all developed problems fall into the valid category. The developed problems are also highly reliable, with a reliability coefficient of . Therefore, it is concluded that this development research produces 36 AKM-based problems to measure students' numeracy literacy skills in statistics that are valid and reliable.

This study examines the legal istinbath method applied by Imam Syafi'i, especially in the context of solving sexual harassment cases in Indonesia. Legal identity, which etymologically means the excavation of law by deep reasoning, is used to determine the law in matters that are not directly regulated by the Qur'an and Hadith. Imam Shafi'i, through his major works such as "Al-Umm" and "Al-Risalah," explains the basic principles and methodologies used to establish the law by incorporating the main sources of Islamic law, namely the Qur'an, Hadith, Ijma', and Qiyas. This study uses a qualitative method with descriptive analysis of primary and secondary sources, including books and scientific articles that discuss the istinbath method of Imam Shafi'i. The results of the study show that the legal principles generated by this method are very relevant and adaptive in dealing with modern cases such as sexual harassment, which is often triggered by patriarchal culture. Imam Shafi'i's method of legal istinbath, which prioritizes the hierarchy of legal sources and the use of sharp reason, has proven to be able to adapt to the times and continues to be useful in solving modern legal problems. This research also highlights the views of contemporary scholars who provide a new interpretation of this classical method, demonstrating the relevance and effectiveness of the legal istinbath method in dealing with contemporary issues. Thus, this study concludes that the istinbath method of Imam Shafi'i law is a very useful tool to ensure justice and benefits in solving sexual harassment cases in the modern era.

Problem Based Learning (PBL) is a teaching and learning process in the classroom where students are first asked to observe a phenomenon. Then students are asked to record the problems that arise, after that the teacher's job is to stimulate critical thinking in solving existing problems. The teacher's task is to direct students to ask questions, prove assumptions, and listen to different perspectives among them. The problems in this study are (1) Can Problem-Based Learning (PBL) improve student learning outcomes in Civics class V at SD Negeri 15 Pekanbaru (2) How is the effect of student learning outcomes with the Problem-Based Learning (PBL) model in Civics class V at SD Negeri 15 Pekanbaru. This research includes Classroom Action Research (PTK) which was conducted in two cycles using the Problem-Based Learning (PBL) method. Each cycle consists of four stages, namely design, implementation, observation, and reflection. The subjects of this research were fifth-grade students of SD Negeri 15 Pekanbaru, totaling 35 students. The research data was obtained using teacher and student observation sheets and student test results, then the data was analyzed using the percentage formula. The results obtained were (1) teacher activity in cycle I using a problem-based learning model from 78.75% to 91.25% in cycle II, (2) student activity in cycle I using the Problem-Based Learning (PBL) model 50.48% to 85.26%, and, (3) student learning outcomes in Civics subjects in cycle I using problem-based learning 40% to 94.28% in cycle II. This shows that student learning outcomes in Civics subjects using problem-based learning models show very positive results. Based on the results of this study can improve student learning outcomes to be more active and the ability of teachers to improve for the better.      

This study aims to determine the difficulties of students in solving Higher Order Thingking Skills (HOTS) problems by using the Polya method in Trigonometric comparison materials. This research is a descriptive qualitative research. The subjects of the study were 36 students in class X.1 of SMA Negeri 2 Situbondo. Data collection techniques use test questions, interviews and documentation. The test in the form of Higher Order Thingking Skills (HOTS) questions is carried out to measure students' abilities. Interviews were conducted on 6 students based on the category of ability level of test results. Data analysis was carried out using data induction and reduction theory. The test results showed that those who scored in the high-level category were 10 students (28%), the moderate-level category was 14 students (39%) and the low-level category was 12 students (33%). The conclusion of this study states that the difficulty of students in solving Higher Order Thinking Skills (HOTS) questions using the polya method, namely subjects with high-level categories, experience difficulties at the re-examination stage. Subjects with a moderate level category, experienced difficulties at the stage of implementing the plan and re-examining. Subjects with low-level categories experienced difficulties at all stages of polya, namely at the stage of understanding the problem, making a plan, implementing the plan and re-examining.

Teenage non-commissioned officers face several challenges in managing their emotions, which can hinder their ability to perform their duties optimally. One of the main challenges is lack of experience. As newcomers, young non-commissioned officers may not be used to dealing with various stressful, dangerous situations or involving interactions with the public. Emotion management training is expected to provide a number of important benefits for juvenile non-commissioned officers and the police institution as a whole. One of the main benefits is increased performance. To achieve the expected goals and benefits, the implementation of emotion management training must be carried out systematically and continuously. Training can begin with an introductory session on the importance of managing emotions, followed by practical training on communication skills, problem solving, and relaxation techniques. In addition, training should include simulations of real situations that youth NCOs may encounter, so that they can apply the skills learned in relevant contexts. Training evaluations must be carried out periodically to ensure that training objectives are achieved and the expected benefits can be felt. Evaluation can be done through knowledge tests, performance observations, and participant satisfaction surveys. Overall, this emotion management training provides short-term benefits in the form of reduced stress and improved performance, while also providing youth non-commissioned officers with skills that are crucial for their long-term careers in the police force. Thus, investment in the development of these skills not only improves operational efficiency but also supports the psychological well-being and professionalism of future police officers.

This research aims to analyse students' mathematical problem solving ability on length and weight measurement material in class III at SD Negeri Langgenharjo 01. This type of research is a qualitative descriptive research. The data source of this research comes from the answers to the mathematical problem solving ability description test and interviews. This study used 3 subjects from 30 grade III students who were taken using purposive techniques according to the category of mathematical problem solving ability, consisting of high, medium, and low categories. Data collection techniques used observation, interviews, and documentation. The data analysis technique used in this study used the Miles and Huberman model, namely, data collection, data reduction, data presentation, and conclusion drawing. Based on the results of research on mathematical solving ability according to Polya's level, namely, (1) Students in the high category are able to fulfil all four indicators of problem solving according to Polya's stages. (2) Students in the medium category can solve problems well, but are often less careful and often hasty. They can only fulfil 2 of the 4 problem solving indicators. (3) Students in the low category have not been able to solve the problem well. They were unable to fulfil all indicators of problem solving ability according to Polya's stages. The conclusion of this study is that students have various potentials in mathematical problem solving ranging from high, medium, and low categories.

Lower elementary school students usually have difficulty solving arithmetic puzzles. This is caused by variables inhibiting students, including lack of focus and low motivation to learn. This research was conducted to determine the proficiency of class II students at SD 1 Selojari in answering addition and subtraction questions through the use of narrative questions. The aim of the qualitative method of this research which uses a qualitative descriptive approach is to characterize mathematical problem solving abilities. The technique for selecting subjects in this research is using a purposive sampling technique, which is a technique for determining samples with various specific considerations using 11 class II students at SD 1 Selojari. The data collection techniques used were interview, observation and documentation methods. The data analysis technique uses data collection, data reduction, and drawing conclusions.  The mathematical problem solving ability of second grade elementary school students in addition and subtraction material is quite high, namely 90%, as seen in the students' ability to work on the questions given and get high scores. The results of this research show that one in three students are still unable to solve problem questions and still need help.

Students need to have mathematical problem-solving skills to solve mathematical problems both in school and in real life. But in reality, students' mathematical problem-solving skills are still low. This study aims to analyze students' mathematical solving abilities from the perspective of gender differences, so that teachers can find the right solutions to improve students' abilities. This research is a qualitative research. The instruments used in this study are test questions and interview guidelines. The subjects of this study were three students taken from 20 students in grade VIII MTs Azzainiyah II. The subject consists of one student representing each of the high, medium, and low abilities. The results of the study showed that the mathematical solving ability of female students was better than that of male students. In the group of high-ability students, female students can meet all four indicators of the mathematical problem-solving stage, while male students can only meet the three indicators of the mathematical problem-solving stage. In the group of moderate-ability students, female students can meet three indicators of the mathematical problem-solving stage, while male students can only meet two indicators of the mathematical problem-solving stage. In the group of low-ability students, female students can meet two indicators of the mathematical problem-solving stage, while male students can only meet one indicator of the mathematical problem-solving stage.