This final project examines the dynamics of the Fermi-Pasta-Ulam-Tsingou-α (FPUT-α) system, focusing on double-mode excitations and the equipartition of energy phenomenon. Through numerical simulations, it is investigated how variations in initial energy and excitation mode combinations influence energy distribution among modes. The results show that at low energy levels, energy remains uneve…
This final project discusses the development of mixtilinear incircle on angle trisectors in morley triangles. An angle trisector is defined as a line that divides an angle into three equal parts. If an angle is divided by two trisector lines, then each part of the resulting angle has the same size, which is one-third of the original angle. Mixtilinear incircle are internally tangent to the side…
This study discusses the implementation of block matrix inversion in input- output analysis of domestic transactions in Indonesia. A block matrix is a large matrix composed of smaller submatrices, used to simplify the inversion process in domestic transaction tables. The constructed block matrix is then analyzed using input-output analysis to measure the extent to which one sector influences an…
This final project discusses the modification of the Simpson’s 1/3 rule for approximating the Riemann-Stieltjes integral. The modification involves de- termining the coefficients of a monomial function of a certain degree, resulting in a second-order accuracy. The error is derived from the difference between the exact solution and the approximate solution. Numerical tests on several nonlinear…
This final project discusses the recovery of energy recurrence in a heterogeneo- us FPUT-β system with parameter variability. The tolerance values considered include 5%, 10%, 50%, and 95%. Moreover, several tolerance distributions su- ch as random, ascending, and centrosymmetric are introduced as approaches to restore energy recurrence in the FPUT-β system. The FPUT-β system is solved numeri…
This final project discusses three forms of iteration methods developed using the homotopy perturbation technique to solve nonlinear equations. The derivation of this method utilizes the Newton method approach, which is then improved by the homotopy perturbation technique so that a power series solution is obta- ined which forms three new iteration methods. Convergence analysis based on Taylor …
This final project discusses the Hamiltonian cycle on a new graph, namely the wijaya kusuma flower graph which is constructed by representing the original wijaya kusuma flower structure into a graph form. The vertex set V represents the flower structure such as the pistil, stamen, petals, and sepals, while the edge set E represents the relationship among these components. A Hamiltonian cycle is…
Adenovirus is a DNA virus that causes infections in the upper or lower respira- tory tract, pharynx, gastrointestinal tract, and conjunctiva. Let G = (AVn) be the modified adenovirus graph, which is constructed from molecular biology da- ta, where V (G) is the set of vertices representing genes of the DNA virus, DNA segments, and their variants, while E(G) is the set of edges representing over-…
This final project discusses modified Wu’s method, Liu’s method, Dˇzuni´c’s me- thod, and their combinations by updating several parameters to develop new methods. Analytically it is shown that the methods is convergence of order four. A memory acceleration technique is applied to enhance the convergence of these fourth-order methods. Computational tests using three tests functions and …
This final project discusses the modification of the Chebyshev method by adding the parameter p to obtain a new iteration method. Analysis of the convergen- ce order shows that this method has a convergence order of three. The basic characteristics of this method indicate that increasing the value of the para- meter p can speed up the computation. Computational tests show that the proposed meth…
This final project discusses a predator–prey dynamic model with delay-induced effects, incorporating a fear effect on the prey and intraspecific competition within the predator species. For the system without delay, three equilibrium points are obtained, namely two saddle points and one whose stability depends on certain parameters. In the delayed system, there exists a critical delay thre- s…
This study aims to produce a higher Order Thinking Skills (HOTS) instrument that is valid, reliable, has a good discriminating power and difficulty level in order to train high-level thinking skills of Phase D students. Penelitian ini menggunakan model pengembangan tipe development studies yang terdiri dari dua tahapan yaitu preliminary yang terbagi menjadi analysis dan desain, serta formative …
This study aimed to enhance the learning process and enhance students' learning results in mathematics by implementing the Problem Based Learning approach. Students are encouraged to actively engage in the learning process through this approach of instruction. This study is a classroom action research using observation sheets of teacher and student activities and mathematics learning outcom…
The low achievement of Learning Objective Achievement Criteria (KKTP) in mathematics among students in class VII-1 at SMPN 19 Pekanbaru served as the background for conducting this research. This classroom action research aimed to improve mathematics learning outcomes and enhance the learning process through the implementation of the Problem Based Learning (PBL) model. The research design emplo…
This study was motivated by the low mathematical problem-solving Skills of students caused by inappropriate learning approaches, as well as the lack of teaching materials that support the development of mathematical problem solving skills. This study aims to produce mathematics teaching materials based on a scientific approach that is valid and practical to facilitate students' mathematical…
This final project discusses of the Leslie matrix to estimate the population growth rate of women in Riau Province. This research uses a quantitative method with secondary data obtained from the Riau Province Central Bureau of Statistics for the years 2015–2020, consisting of data on the female population and birth rates. The Leslie matrix is constructed based on age structure, fertility …
This final project discusses a family of iteration methods using weight functions to solve nonlinear equations. Certain weight functions are chosen to obtain some existing methods and a new iteration methods as a special case. Analytically, this family of iteration methods has a convergent order of five with an efficiency index of 1.495. Computational tests show that the new methods in this fam…
Penelitian ini dilatarbelakangi dengan pentingnya kemampuan komunikasi matematis dimiliki oleh peserta didik karena; (a) matematika adalah bahasa esensial yang tidak hanya sebagai alat berpikir, menemukan rumus menyelesaikan masalah, atau menyimpulkan saja, namun matematika juga memiliki nilai yang tak terbatas untuk menyatakan beragam idea secara jelas, teliti dan tepat; (b) matematika dan bel…
Penelitian ini dilatarbelakangi oleh hasil belajar peserta didik kelas X.4 SMA Negeri 7 Pekanbaru yang belum memenuhi Kriteria Ketercapaian Tujuan Pembelajaran (KKTP) yang telah ditetapkan yaitu 78. Hasil tes awal yang dilakukan oleh peneliti kepada peserta didik sebelum diberikan tindakan, dari 36 peserta didik yang mengikuti tes hanya 11 orang atau 30% yang nilainya mencapai KKTP yang telah d…
The problem in this research is that students' level of mathematical problem solving ability (KPMM) is low, while it is important for students to master KPMM in learning mathematics. Therefore, the aim of carrying out this research is to produce learning tools on two-variable linear equation systems material to facilitate KPMM for class VIII SMP/MTs students. The research trial involved subject…