PENYELESAIAN MASALAH INFILTRASI DARI SALURAN DATAR PERIODIK MENGGUNAKAN DUAL RECIPROCITY BOUNDARY ELEMENT METHOD DENGAN FUNGSI BASIS RADIAL

This research discusses the numerical solution of the infiltration problem of the periodic flat channel and is solved using the Dual Reciprocity Boundary Element Method (DRBEM)  numerical method with polynomial radial basis functions. DRBEM is a development of the Boundary Element Method, used for PDP solutions in the fields of mathematical physics and engineering. DRBEM has an important role in obtaining a solution to the Helmholtz equation by describing the reciprocal relation between the fundamental solution of the Laplace equation and the solution to be sought. Furthermore, the term containing the double integral in the calculation is approximated by the radial basis function, in order to obtain an equation containing only the boundary integral. The objective of the obtained numerical solution is then compared with the analytical solution obtained by Batu, in order to obtain an accurate solution of the polynomial radial base function for solving the infiltration problem. The mathematical models used in the infiltration problem are the Richards equations, Kirchoff transformation and the dimensionless variables for obtaining the modified Helmholtz equation. The results of the calculation of the numerical solution have shown that the DRBEM with the radial polynomial base function for the number of boundary elements resulting from the discretization and the number of interior collocation points at (N = 200, L = 400) and (N = 225, L = 400) obtained the approximate value ( error) from the six points in the region, indicating that the greater the value of N, the smaller the error. So that for FBR, and  the one with the smallest error is , it means that it is close to the FBR used by Batu, is .. Thus, it is concluded that the more discrete line segments result in the region boundary, the numerical solution will approximate the analytical solution. Keywords: Infiltration, modified Helmholtz equation, FBR, DRBEM.Abstrak Penelitan ini mengkaji mengenai solusi numerik masalah infiltrasi dari saluran datar periodik menggunakan metode  Dual Reciprocity Boundary Element Method (DRBEM) dengan fungsi basis radial polinomial. DRBEM merupakan pengembangan dari Metode Elemen Batas, digunakan untuk penyelesaian PDP pada bidang fisika matematis dan teknik. DRBEM mempunyai peranan penting untuk memperoleh solusi persamaan Helmholtz dengan mendeskripsikan relasi reciprocal antara solusi fundamental persamaan Laplace dan solusi yang akan dicari. Selanjutnya, suku yang memuat integral lipat dua (double integral) dalam perhitungannya didekati dengan fungsi basis radial, agar didapat persamaan yang hanya memuat integral batas. Tujuan dari solusi numerik yang diperoleh selanjutnya dibandingkan dengan solusi analitik yang diperoleh Batu, agar diperoleh solusi yang akurat dari fungsi basis radial polinomial untuk penyelesaian masalah infiltrasi tersebut. Model matematika yang digunakan adalah persamaan Richards dan transformasi Kirchoff serta variabel-variabel tak berdimensi menjadi persamaan Helmholtz termodifikasi. Hasil perhitungan solusi numerik telah memberikan hasil bahwa DRBEM dengan fungsi basis radial polinomial tersebut untuk jumlah  boundary element  hasil diskritisasi dan jumlah titik kolokasi interior pada (N=200, L=400) dan (N=225, L=400) diperoleh nilai pendekatan (error) dari keenam titik di region, menunjukkan semakin besar nilai N maka semakin kecil  errornya. Sehingga untuk FBR , dan  yang memiliki error terkecil adalah  artinya mendekati FBR yang digunakan oleh Batu, yakni . Dengan demikian, disimpulkan bahwa semakin banyak ruas garis hasil diskritisasi pada batas region, solusi numerik akan mendekati solusi analitiknya

Model Regresi Dummy Indeks Prestasi Akademik Mahasiswa Program Studi Matematika Faperta Unimor

One indicator that can be used as a determinant in the quality of higher education is the academic achievement of students. Grade Point Average (GPA) is a measure of the academic performance. GPA gained students can not be separated from the quality of the incoming student input at the college. This study discusses some of the indicators that can be used as a measure of the quality of student input from the academic side, such as the National Examination (NE), the origin of school (public / private), gender and type of college entrance exam (SNMPTN test, SBMPTN test and independent institution test). Because some of these indicators are qualitative so the data analysis used regression analysis with dummy variables. Research conducted on students of Mathematics Study Program, Faculty of Agriculture, Timor University, class of 2017 to class of 2021. From the data processing, obtained regression model: . From the data analysis, concluded that the female students of Mathematics Study Program, Faculty of Agriculture, Timor University, coming from public schools and type of college entrance exam is SNMPTN have the greatest tendency to obtain high GPA compared with other students. In addition,  for the regression equation obtained above was 38.2% means that the independent variable in the model can explain the diversity of the GPA of 38.2%

Pelatihan Pembuatan Aplikasi E-raport dengan Menggunakan Microsoft Office Excel Bagi Guru-guru SD di Wilayah Insana Fafinesu

The activity of filling in school data, student data, and student final grades in report card at elementary schools in the Insana Fafinesu District, Timor Tengah Utara Regency has been carried out in handwriting (conventional), which have some constraints such as taking a long time to processing grades, has a tendency to miscalculation if the student report card is lost or damaged, it does not have documentation/ back-up documents. For teachers who have sloppy handwriting, it will be difficult for a parent to read. One software that can be used in making student report cards is Microsoft Office Excel. This software is easy to understand and can overcome problems in making student report cards such as the length of time for processing grades, the tendency of grade processing error, difficulties in reading teacher writing by parents, and overcoming problems with documentation/backup documents. This service activity aims to provide training in making e-report card applications using Microsoft Excel for elementary school teachers in the Insana Fafinesu area, Timor Tengah Utara Regency. The methods used in this activity are workshops and ongoing mentoring. As a result, teachers better understand the functions in Microsoft Excel that are useful in the process of filling out student report cards, each teacher succeeds in making their own e-reports, and they agree that e-reports with Microsoft Excel are more efficient and effective than filling out report cards manually (conventional) and will use e-reports in their respective schools. The next plan for this service activity will be an application for Teacher Performance Assessment (TPA) and Employee Work Targets (EWT). &nbsp

Analisis Sistem Antrian dalam Optimalisasi Layanan pada Jabalmart Kefamenanu

The number of visitors who come to Jabalmart Kefamenanu causes a long queue in front of the cashier. Queuing discipline applied at Jabalmart Kefamenanu is First In First Out, that is customers who come first will be served first. The form of the queuing model in this study at Jabalmart Kefamenanu is a single-phase multi-chanel, namely two or more service facilities and flows through a sibgle line. The purpose of this research is to optimize service at the cashier at Jabalmart Kefamenanu. As for the results of this study, the average service time at each cashier is quite effective because each cashier has a level of service intensity (. That is cashier I level of service intensity () is 0,63, cashier II level of service intensity () is 0,6 and cashier III level of service intensity () is 0,231, it can be concluded that the optimal level of service at the Jabalmart Kefamenanu cashier is quite effective and has been said to be optimal

Optimasi Penugasan Pekerja Menggunakan Metode Hungarian Modifikasi pada Proyek Pembangunan Jembatan X di Kabupaten Timor Tengah Utara

Assignment problems that are often encountered in local life are problems related to the optimal allocation of various productive resources or personnel that have different levels of efficiency for different jobs. The Hungarian method can be used to solve balanced assignment problems, namely the number of workers is equal to the number of jobs and unbalanced assignments, and namely the number of workers is not the same as the number of jobs. The assignment problem in this study is an unbalanced assignment problem where the number of workers is 90 (ninety) people divided into 4 (four) work teams while the number of work items is as much as 7 (seven) work items. This assignment can be completed by applying a modified Hungarian method with the aim of minimizing work completion time, worker wages and minimizing completion time and worker wages together. From the research results, after using the modified Hungarian method, the optimal total time is 25 days with the optimal total cost of IDR 57,080,000 and the combined completion time and total wages calculated jointly is 87.3

Analisis Sistem Pembayaran Kredit di KSP Kopdit Swasti Sari Cabang Atambua Menggunakan Persamaan Beda Linear Orde Satu

ABSTRACT Giving credit is a business activity that contains a high risk and affects the sustainability of businesses such as cooperatives and banking. The aims of this research are to: (a) knowing the credit decision making system implemented in KSP Kopdit Swasti Sari, (b) knowing the calculation of the remaining credit payments using the first-order linear difference equation. In this study, the method used to calculate the remaining debt for credit payments is a first-order linear difference equation, namely the remaining debt after the first payment is the same as the remaining debt after payment to t plus interest minus annuity. The results of this study indicate that the credit decision-making process is considered worthy of receiving a credit loan if it meets the requirements that have been set at the KSP Kopdit Swasti Sari. The step to calculate the remaining credit payments using a mathematical model is to find the amount of fixed installments from an ordinary annuity with a different loan size, namely Rp 5.000.000, Rp 10.000.000 and Rp 15.000.000. After getting the results from the ordinary annuity, a mathematical model of the remaining credit payments is formed using equation (2.13). The results of the calculation of the remaining credit payments using a mathematical model are as follows: For the first order linear difference equation with a loan size of Rp 5.000.000 after paying the first installment () the remaining debt is Rp 4.900.081 and the remaining debt () of Rp. 8. For a large loan of Rp. 10.000.000 after paying the first installment () the remaining debt is Rp. 9.800.162 and on payment of () the remaining debt is Rp. 16. For a large loan of Rp 15.000.000 after paying the first installment () the remaining debt is Rp  14.700.243 and on payment of () the remaining debt is Rp 24.ABSTRAK Pemberian kredit merupakan kegiatan usaha yang mengandung resiko tinggi dan berpengaruh terhadap keberlangsungan usaha seperti koperasi dan perbankan. Tujuan penelitian ini adalah untuk: (a) mengetahui sistem pemberian keputusan kredit yang diterapkan di KSP Kopdit Swasti Sari Cabang Atambua, (b) mengetahui perhitungan sisa pembayaran kredit menggunakan persamaan beda linear orde satu. Dalam penelitian ini metode yang digunakan untuk menghitung sisa  hutang pembayaran kredit adalah persamaan beda linear orde satu yaitu sisa hutang setelah pembayaran pertama sama dengan sisa hutang setelah pembayaran ke  ditambah bunga dikurangi anuitas. Hasil penelitian ini menunjukkan proses pemberian keputusan kredit dianggap layak menerima pinjaman kredit jika sudah memenuhi syarat-syarat yang sudah ditetapkan di KSP Kopdit Swasti Sari. Langkah untuk menghitung sisa pembayaran kredit menggunakan model matematika yaitu mencari besar angsuran tetap dari anuitas biasa dengan besar pinjaman yang berbeda yaitu Rp 5.000.000, Rp 10.000.000 dan Rp 15.000.000. Setelah mendapatkan hasil dari anuitas biasa dibentuk model matematika sisa pembayaran kredit menggunakan persamaan (2.13). Hasil perhitungan sisa pembayaran kredit dengan menggunakan model matematika sebagai berikut: Untuk persamaan beda linear orde satu dengan besar pinjaman Rp 5.000.000 setelah dibayar angsuran pertama () sisa hutangnya sebesar Rp 4.900.081 dan sisa hutang ) sebesar Rp 8. Untuk besar pinjaman Rp 10.000.000 setelah dibayar angsuran pertama ( sisa hutangnya sebesar Rp 9.800.162 dan pada pembayaran ) sisa hutang sebesar Rp 16. Untuk besar pinjaman Rp. 15.000.000 setelah dibayar angsuran pertama ( sisa hutangnya sebesar Rp 14.700.243 dan pada pembayaran ) sisa hutang sebesar Rp 24

Pengembangan Program Linear Multi-Objektif Fuzzy Stokastik Model Simetris dan Penyelesaiannya dengan Menggunakan Teknik Chance Constrained

Linear programming is one method oto determine the optimum value of a problem. Problems of the linear program faced by the decision makers have various variations from time to time. A variety of problems that can be seen as a multi-objective fuzzy linear programming, muli-objective stochastic linear programming, or a combination of both. This study focus on Multi-Objective Fuzzy Stochastic Linear Programming (MOFSLP) with each objective function has a same level of importance for decision makers or name as symmetrical model. The objective function of the MOFSLP contains the fuzzy parameters and normally distributed random variables while the function of constraints contains the fuzzy parameters. The purpose of this research is to formulate MOFSLP and develop algorithms to transform MOFSLP be Single-Objective Deterministic Linear Programming (SODLP) which can be solve using the simplex method. In transforming MOFSLP to SODLP, symmetrical model and also the chance constrained technique are used. In the end of this research, a numerical example is provided to illustrate the algorithm that has been developed. The models and algorithms that have been formed are expected to help decision makers in solving a problem.Program linear merupakan salah satu metode penentuan nilai optimum dari suatu persoalan. Persoalan-persoalan program linear yang dihadapi para pengambil keputusan mengalami berbagai variasi dari waktu ke waktu. Berbagai masalah yang ada dapat dipandang sebagai program linear multi-objektif fuzzy, program linear muli-objektif stokastik, ataupun kombinasi keduanya. Penelitian ini berfokus pada Program Linear Multi-Objektif Fuzzy Stokastik (PLMOFS) dengan setiap fungsi tujuan memiliki tingkat kepentingan yang sama bagi pengambil keputusan atau disebut dengan model simetris. Fungsi tujuan dari PLMOFS ini mengandung parameter fuzzy dan variabel random berdistribusi normal sedangkan fungsi kendalanya mengandung parameter fuzzy. Tujuan dari penelitian ini yaitu memformulasikan PLMOFS dan menyusun algoritma untuk mentransformasi PLMOFS menjadi Program Linear Single-Objektif Deterministik (PLSOD) yang kemudian dapat diselesaikan menggunakan metode simpleks. Dalam mentransformasi PLMOFS menjadi PLSOD digunakan teknik chance constrained. Pada akhirnya diberikan contoh numerik untuk mengilustrasikan cara penyelesaian dari algoritma yang telah disusun. Model dan algoritma yang telah dibentuk diharapkan dapat membantu pengambil keputusan dalam menyelesaikan berbagai persoalan

PENERAPAN METODE SIMPLEKS UNTUK MEMPEROLEH KEUNTUNGAN MAKSIMUM PADA PENJUALAN SIRIH DAN PINANG DI KABUPATEN MALAKA (Studi kasus: Pasar Bei Abuk, Desa Wehali, Kecamatan Malaka Tengah)

Permasalahan yang dihadapi oleh penjual sirih dan pinang Kabupaten Malaka adalah penjualan sirih danpinang secara terpisah yang lazim dilakukan oleh para penjual sirih dan pinang di daerah lainnya. Strategipenjualan seperti ini menyebabkan keuntungan yang diperoleh para penjual tidak optimal. Tujuan daripenelitian ini adalah memberikan strategi penjualan sirih dan pinang menjadi satu tumpukan atau disebut jugadengan kolaborasi antara sirih dan pinang. Metode yang digunakan dalam penelitian ini adalah metodesimpleks. Hasil yang diperoleh sebelum memberikan strategi penjualan kolaborasi antara sirih dan pinangmenjadi satu tumpukan dan menerapkan metode simpleks, keuntunga yang diperoleh dari penjualan sirih danpinang secara terpisah rata-rata sebesar Rp 2.500.000,00 dalam satu bulan. Setelah memberikan strategipenjualan sirih dan pinang yang dikolaborasikan menjadi satu tumpuka serta menerapkan metode simplekskeuntungan yang diperoleh rata-rata sebesar Rp 4.851.000,00 dalam satu bulan