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JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI

jmsk
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Published by Universitas Hasanuddin

ISSN : 18581382 EISSN : 26148811 DOI : -

Core Subject : Education,

Mathematics

Jurnal ini mempublikasikan paper-paper original hasil-hasil penelitian dibidang Matematika, Statistika dan Komputasi Matematika.

Arjuna Subject : -

Articles 496 Documents

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Solusi Numerik Persamaan Differensial Biasa Dengan Menggunakan Metode Predictor – Corrector Agustinus Ribal; Khaeruddin Khaeruddin
Jurnal Matematika, Statistika dan Komputasi Vol. 5 No. 2: January 2009
Publisher : Department of Mathematics, Hasanuddin University

Dalam tulisan ini akan diperkenalkan suatu solusi numerik dari persamaan differensial biasa order pertama dengan menggunakan metode predictor-corrector. Pertama-tama formula predictor akan ditentukan, kemudian menurunkan predictor formula untuk Adam-Bashforth beserta dengan corrector formulanya dimana corrector formula akan digunakan untuk mengoreksi nilai yang telah diprediksi. Selanjutnya, perulangan corrector akan dilakukan. Metode Runge Kutta orde keempat akan digunakan sebagai nilai awal dari metode predictor.

Modifikasi Penaksir Robust dalam Pelabelan Outlier Multivariat Erna Tri Herdiani; Nirwan Ilyas
Jurnal Matematika, Statistika dan Komputasi Vol. 14 No. 1 (2017): July 2017
Publisher : Department of Mathematics, Hasanuddin University

Outlier adalah suatu observasi yang polanya tidak mengikuti mayoritas data. Outlier dalam kasus multivariat sangat sulit untuk dideteksi, khususnya ketika dimensi lebih dari 2. Kesulitan ini meningkat ketika data set berukuran besar, yakni jumlah variabel menjadi besar. Metode-metode pendeteksian outlier telah lama berkembang dan beberapa digunakan untuk pelabelan outlier sehingga data dapat dipisahkan antara data yang dicurigai sebagai outlier dan data set pada umumnya. Metode-metode tersebut adalah minimum volume ellipsoid disingkat MVE, minimun covariance determinant disingkat MCD, dan minimum vector variance disingkat MVV. Dari ketiga metode tersebut MVV memiliki waktu perhitungan yang paling cepat. Berdasarkan algoritma MVV, kriteria mengurutkan data menggunakan jarak mahalanobis, maka pada paper ini akan dimodifikasi kriteria pengurutan data dengan menghindari penulisan dalam bentuk invers dari matriks variansi kovariansi. Hasil yang diperoleh adalah metode MVV menjadi lebih cepat dengan menggunakan kriteria baru dengan kecermatan yang sama dengan MVV sebelumnya serta akan diaplikan untuk data real dan data simulasi.

ANALISIS KEMAMPUAN PEMECAHAN MASALAH BERDASARKAN MINAT BELAJAR MATEMATIKA SISWA SMA PEKANBARU PADA MATERI SPLTV Lusi Wira Aftriyati; Yenita Roza; maimunah maimunah
Jurnal Matematika, Statistika dan Komputasi Vol. 16 No. 2 (2020): JMSK, JANUARY, 2020
Publisher : Department of Mathematics, Hasanuddin University

The problem solving abilities of students in learning mathematics are still not well trained, and there are varying degrees of difficulty experienced by students in learning mathematics. Factors that influence the ability to solve problems include interest in learning. This study aims to analyze the ability of problem solving based on students' interest in learning mathematics. This type of research is a descriptive qualitative study, which was conducted at Babussalam Pekanbaru High School with research subjects coming from Class X MIPA 1 selected based on the level of problem solving skills and student interest in learning. Problem solving abilities consist of categories: high, medium, low. Learning interest is categorized as positive and negative interests. Data collection techniques are written tests and non-tests in the form of questionnaire interest in learning and interviews. Based on the research results, the problem solving ability of high category students with positive learning interest is able to meet all indicators of problem solving ability. The problem solving ability of the medium category students with positive learning interest is able to meet the indicators of planning for solving, solving problems, and checking. The problem solving ability of low category students with positive learning interest is only able to meet the indicators of planning a solution, and solving a problem. The ability of problem solving students in the moderate category with negative learning interest is able to meet the indicators of planning for solving, solving problems, and checking.

Analisis Kestabilan Model Logistik Satu Populasi Dengan Tundaan Waktu Syamsuddin Toaha
Jurnal Matematika, Statistika dan Komputasi Vol. 8 No. 2: January 2012
Publisher : Department of Mathematics, Hasanuddin University

Dalam tulisan ini dibahas model logistik satu populasi dengan tundaan waktu. Tundaan waktu dipertimbangkan dalam model karena laju perubahan suatu populasi tidak hanya bergantung pada jumlah populasi pada saat sekarang tetapi juga bergantung pada jumlah populasi pada waktu lampau. Pada tulisan ini pengaruh tundaan waktu terhadap kestabilan titik keseimbangan model dianalisis dengan menggunakan pendekatan deret Taylor di sekitar titik keseimbangan. Dengan pendekatan itu diperoleh suatu model tanpa bentuk jumlah populasi yang bergantung pada tundaan waktu tetapi model tersebut tetap bergantung pada tundaan waktu. Penyelesaian analitik untuk model tersebut diberikan. Dari penyelesaian analitik itu diketahui bahwa titik keseimbangan positif stabil untuk suatu kondisi tundaan waktu dan jumlah awal populasi tertentu..

Identifikasi Lokasi Sebaran Pencemaran Air di Kawasan Permukiman Kota Pontianak Naomi Nessyana Debataraja; Dadan Kusnandar; Rossie Wiedya Nusantara
Jurnal Matematika, Statistika dan Komputasi Vol. 15 No. 1 (2018): July 2018
Publisher : Department of Mathematics, Hasanuddin University

Air mempunyai peranan penting bagi aktivitas kehidupan manusia. Aktifitas manusia dalam kehidupan sehari-hari menghasilkan limbah yang berbeda-beda yang dapat mengakibatkan menurunnya kualitas air. Aktifitas manusia dalam kehidupan sehari-hari menghasilkan limbah yang berbeda-beda yang dapat mengakibatkan menurunnya kualitas air. Kota Pontianak sebagai ibukota Kalimantan Barat merupakan daerah yang tingkat pemukimannya cukup padat. Kondisi ini disertai dengan laju pertumbuhan penduduk yang cukup besar. Penelitian ini bertujuan untuk menentukan lokasi untuk pengambilan sampel air dan menentukan variabel sebagai indikator pencemaran air. Teknik pengambilan sampel secara stratified sampling. Variabel yang digunakan dalam menentukan lokasi pengambilan sampel diantaranya adalah batas administrasi, luas wilayah, jumlah penduduk dan kepadatan penduduk. Variabel-variabel tersebut kemudian divisualisasikan dalam bentuk peta tata guna lahan dengan menggunakan Sistem Informasi Geografis (SIG). Diperoleh 58 titik lokasi pengambilan sampel air dan tiga indikator pencemaran air di kawasan permukiman.

APLIKASI KONTROL OPTIMAL PADA PERUBAHAN PERILAKU MANUSIA Sulfayanti Sulfayanti; Syamsuddin Toaha; Khaeruddin Khaeruddin
Jurnal Matematika, Statistika dan Komputasi Vol. 11 No. 1: July 2014
Publisher : Department of Mathematics, Hasanuddin University

Perilaku manusia dapat diartikan sebagai ciri-ciri karakteristik secara prinsipil dapat membedakan manusia yang satu dengan manusia lainnya, sebagai bentuk respon terhadap stimulus yang diberikan. Secara garis besar ada dua faktor yang mempengaruhi perilaku manusia yaitu faktor personal (dari diri sendiri) dan faktor lingkungan. Dalam tulisan ini diberikan suatu model perubahan perilaku manusia dengan memberikan kontrol pada faktor personal dan lingkungan. Penentuan bentuk kontrol optimal tersebut diperoleh melalui penerapan Kalkulus Variasi dan Prinsip Minimum Pontryagin yang kemudian didiskritisasi dengan Metode Beda Hingga. Hasil dari simulasi numerik menunjukkan bahwa pengontrol-pengontrol tersebut dapat menekan laju dari faktor personal dan faktor lingkungan karena mampu mengurangi jumlah individu yang berperilaku buruk.

Non-cash Payment Transaction Projection Using ARIMAX : Efect of Calendar Muhammad Luthfi Setiarno Putera
Jurnal Matematika, Statistika dan Komputasi Vol. 16 No. 3 (2020): JMSK, MAY, 2020
Publisher : Department of Mathematics, Hasanuddin University

As the most Moslem country, economic activity in Indonesia is often parallel with the movement of Qamariah (lunar) calendar which is different with Gregorian calendar. Using calender variation, this research attempts to look for modified time series model for non-cash payment projection (forecast) aim. The result shows that calendar variation plays statistically significant role on non-cash payment, evidenced by significant payment in the month in which Eid Fitr occurs. The occurrence of Eid Fitr in the first and second week of the month is evidently characterized by increasing non-cash payment in one month earlier. The best model with highest accuracy for non-cash payment projection is ARIMAX(2,1,1) as it is able to capture the pattern, trend and fluctuation. It also suggests the peak of non-cash payment will be in December.

Optimal control for SIR Model with The Influence of Vaccination, Quarantine and Immigration factor Susi Agustianingsih; Rina Reorita; Renny Renny
Jurnal Matematika, Statistika dan Komputasi Vol. 16 No. 3 (2020): JMSK, MAY, 2020
Publisher : Department of Mathematics, Hasanuddin University

The SIR model is one of the mathematical model which describes the characteristic of the spread of infectious disease in differential equation form by dividing the human populations into three groups. There are individual susceptible group, individual infective group, and individual recovered group. This model involves vaccination, quarantine, and immigration factors. Vaccination and quarantine must be given as much as it needs, so a control is required to minimize infection of disease and the number of individual infective with a minimum costs. In this research, optimal control of SIR model with vaccination, quarantine, and immigration factor is solved by using Pontryagin maximum principle and numerically simulated by using Runge-Kutta method. Numerical simulation results show optimal control of treatment, citizen of vaccination, immigrant of vaccination, and quarantine will accelerate the decline of infected number with the minimum cost, compared with the optimal control of SIR model without quarantine factor.

Partition Dimension of Complete Multipartite Graph Safriadi Safriadi; Hasmawati Hasmawati; Loeky Haryanto
Jurnal Matematika, Statistika dan Komputasi Vol. 16 No. 3 (2020): JMSK, MAY, 2020
Publisher : Department of Mathematics, Hasanuddin University

Determining a resolving partition of a graph is an interesting study in graph theory due to many applications like censor design, compound classification in chemistry, robotic navigation and internet network. Let and , the distance between an is . For an ordered partition of , the representation of with respect to is . The partition is called a resolving partition of if all representation of vertices are distinct. The partition dimension of graph is the smallest integer such that has a resolving partition with element.In this thesis, we determine the partition dimension of complete multipartite graph , which is limited by , with and . We found that , , and , .

The solution of nonlinear parabolic equation using variational iteration method wartono wartono; Irma Suryani
Jurnal Matematika, Statistika dan Komputasi Vol. 16 No. 3 (2020): JMSK, MAY, 2020
Publisher : Department of Mathematics, Hasanuddin University

Variational iteration method is a semi analytic solution used to solve the parabolic differential equation both of homogen or nonhomogen. In the process of determining an approximation solution, this method did not use a linearization and a small pertubation. In this paper, the variational iteration method is implemented in the parabolic differential equation in the form of ut = uxx + f(u) + g(x, t) with appropriate intial condition. Furthermore, some examples of special parabolic differential equations are given to test the reliability and convergence of the method. Based on the result of study shows that the variational iteration method is able to solve the parabolic differential equation with a good accuration.

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