Journal of Mathematics Computations and Statistics最新文献

{"title":"Bilangan Kromatik Pewarnaan Titik pada Graf Dual dari Graf Roda","authors":"Muhammad Abdy, Rahmat Syam, T. Tina","doi":"10.35580/jmathcos.v4i2.24443","DOIUrl":"https://doi.org/10.35580/jmathcos.v4i2.24443","url":null,"abstract":"Penelitian ini bertujuan mengkonstruksi graf dual dari graf roda (Wn*) dan menentukan bilangan kromatik graf dual dari graf roda (Wn*). Penelitian ini dimulai dari menggambarkan beberapa graf roda  dari  ke , kemudian membangun graf dual dari graf roda  dengan memanfaatkan graf-graf dari  ke , kemudian memberikan warna pada titik-titik dari graf dualnya dengan menentukan bilangan kromatiknya. Diperoleh hasil bahwa Graf roda  merupakan graf self-dual karena isomorfik dengan graf dualnya yaitu . Pewarnaan titik diperoleh dengan menentukan bilangan kromatik graf dual dari graf roda, menentukan pola dari bilangan kromatik, dan memberikan warna. Berdasarkan hasil penelitian, diperoleh bilangan kromatik pewarnaan titik pada graf dual dari graf roda yakni Kata Kunci: Pewarnaan Titik, Bilangan Kromatik, Graf Dual dan Graf Roda.This research aims to construct a dual graph from a wheel graph (Wn*) and determine the dual graph chromatic number of the wheel graph (Wn*). This research starts from describing some wheel graph   from  to , then construct a dual graph from a wheel graph   from  to , then gives color to the vertices of the dual graph by determining the chromatic number. The result showed that the wheel graph  is a self-dual graph because it is isomorphic with its dual graph, namely . The vertex coloring is obtained by determining the chromatic number of the dual graph of the wheel graph, determining the pattern of the chromatic number and giving the color. Based on the research results, the chromatic number of vertex coloring on dual graph of a wheel graph is:    Keywords: Vertex Coloring, Chromatic Number, Dual Graph and Wheel Graph.","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122372101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solusi Model Perubahan Garis Pantai dengan Metode Transformasi Elzaki","authors":"Maya Sari Wahyuni, S. Sukarna, Muhajir Rosadi","doi":"10.35580/jmathcos.v4i2.24440","DOIUrl":"https://doi.org/10.35580/jmathcos.v4i2.24440","url":null,"abstract":". Pantai merupakan kawasan yang sering dimanfaatkan untuk berbagai kegiatan manusia, namun seringkali upaya pemanfaatan tersebut menyebabkan permasalahan pantai sehingga garis pantai berubah. Salah satu cara yang dapat digunakan untuk mengetahui perubahan garis pantai yaitu dengan membuat model matematika. Model perubahan garis pantai berbentuk persamaan diferensial parsial dapat diselesaikan secara analitik dengan menggunakan metode transformasi Elazki. Metode transformasi Elzaki merupakan salah satu bentuk transformasi integral yang diperoleh dari integral Fourier sehingga didapatkan transformasi Elzaki dan sifat-sifat dasarnya. Perubahan garis pantai pada penelitian ini dipengaruhi oleh adanya groin. Penyelesaian model perubahan garis pantai dengan metode transformasi Elzaki dilakukan dengan menerapkan transformasi Elzaki pada model perubahan garis pantai untuk memperoleh model perubahan garis pantai yang baru, kemudian menerapkan syarat batas, kemudian menerapkan invers transformasi Elzaki sehingga diperoleh solusi model perubahan garis pantai. Berdasarkan hasil penelitian, diperoleh bahwa terdapat kesamaan antara pola grafik yang dihasilkan dari solusi model perubahan garis pantai dengan metode transformasi Elzaki dan solusi model perubahan garis pantai dengan metode numerik.Kata Kunci: Perubahan garis pantai, Groin, Analitik, Transformasi Elzaki.The beach is a region that is often used for various human activities, however often these utilization efforts cause beach problems so that the shoreline changes. One way that can be used to determine changes in shoreline is to make a mathematical model. The shoreline change model shaped of partial differential equation can be solved analytically by using the Elzaki transform method. The Elzaki transform method is a form of integral transform obtained from the Fourier integral so that the Elzaki transform and its basic properties are obtained. Shoreline change in this research were affected by groyne. Solution of shoreline change model using Elzaki transform method is carried by applying the Elzaki transform to the shoreline change model to obtain a new shoreline change model, then applying the boundary value, then applying the inverse of Elzaki transform so obtained a solution shoreline change model. Based on the research result, it was found that there was a similiarity between the graphic patterns generated from the solution of shoreline change model using Elzaki transform method and the solution of shoreline change model using numerical method.Keywords: Shoreline change, Groyne, Analitic, Elzaki transform","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130080732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pemodelan Matematika SIRI pada Penyebaran Penyakit Tifus di Sulawesi Selatan","authors":"Syafruddin Side, A. Zaki, S. Sartika","doi":"10.35580/jmathcos.v4i2.24439","DOIUrl":"https://doi.org/10.35580/jmathcos.v4i2.24439","url":null,"abstract":"Penelitian ini bertujuan untuk membangun model penyebaran penyakit Tifus tipe SIRI (Susceptible-Infected-Recovered-Infected), dengan menambahkan asumsi bahwa manusia yang sembuh dapat kembali terinfeksi penyakit Tifus. Model ini di bagi menjadi 3 kelas yaitu rentan, terinfeksi dan sembuh. Adapun prosedur penelitian dilakukan melalui tahapan-tahapan: membangun model penyebaran penyakit Tifus tipe SIRI, Menguji Kestabilan titik kesetimbangan dan menentukan bilangan reproduksi dasar , kemudian menerapkannya pada kasus Penyakit Tifus di Provinsi Sulawesi Selatan. Data yang digunakan dalam membangun model adalah jumlah penderita penyakit Tifus tahun 2018 dari Dinas Kesehatan Provinsi Sulawesi Selatan. Model matematika tipe SIRI digunakan untuk menentukan titik equilibrium. Berdasarkan hasil simulasi model SIRI diperoleh bilangan reproduksi dasar (  sebesar 0,000903 yang menandakan bahwa penyebaran penyakit Tifus di Provinsi Sulawesi Selatan pada tahun 2018 bukan kejadian luar biasa atau dapat dikatakan bahwa seseorang yang terinfeksi penyakit Tifus ini tidak menyebabkan orang lain terkenapenyakit yang sama, dengan kata lain tidak terjadi wabah pada populasi tersebut.Kata kunci: Titik Equilibrium, Bilangan Reproduksi Dasar, Tifus, Model SIRI. The research aims to build a SIRI model of the Typhoid spread (Susceptible-Infected-Recovered-Infected) by adding assumption that people who are recovered might be infected again. This model is divided into three classes, namely, susceptible, infected and recovered. the research procedure is carried out through several stages: Building SIRI model for the spread of Typhoid, examining the stability of the equilibrium point and determining the basic reproduction number, and applying the model to Typhoid cases in South Sulawesi. The data is the number of Typhus patients in 2018 that was obtained from Health office of South Sulawesi Province. SIRI type mathematical models are used to determine the equilibrium point. Based on the simulation results of the SIRI model, the basic reproduction number is 0,000903 indicate that, indicating that the spread of Typhus in the Province of South Sulawesi in 2018 was not an extraordinary event or it can be said that someone who is infected with this Typhoid does not cause another person to contract the same disease, in other words there was no outbreak in that population.Keywords: equilibrium Point, Basic Reproductive Number, Typhoid, SIRI Model.","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128713641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimasi Pendistribusian Air dengan Metode North West Corner dan Metode Modified Distribution di PDAM Wae Manurung Kabupaten Bone","authors":"Rahmat Syam, Hisyam Ihsan, Muhammad Irham Muktamar","doi":"10.35580/jmathcos.v4i2.24444","DOIUrl":"https://doi.org/10.35580/jmathcos.v4i2.24444","url":null,"abstract":"Penelitian ini membahas tentang optimasi pendistribusian menggunakan model transportasi yang menerapkan Metode North West Corner (NWC) dan Metode Modified Distribution (MODI) pada pendistribusian air di PDAM Wae Manurung kabupaten Bone. Data distribusi air diformulasikan dengan model transportasi, sehiggga diperoleh keseimbangan model dengan penambahan variabel dummy dan tabel transportasi distribusi air, diperoleh solusi awal yang fisibel dengan perhitungan menggunakan Metode North West Corner. Berdasarkan solusi awal diperoleh solusi optimum dengan menggunakan Metode Modified Distribution. Hasil penelitian ini menunjukkan bahwa dengan penerapan Model Transportasi terjadi optimasi biaya distribusi air di Kabupaten Bone sebesar 52,22% dibandingkan hasil perhitungan yang dilakukan oleh PDAM Wae Manurung Kabupaten Bone.Kata Kunci: Optimasi, model transportasi, north west corner, modified distribution, distribusi air This study discusses the Optimization using types of transportation model that application North West Corner method (NWC) and Modified Distribution Method (MODI) on the stock of water in PDAM Wae Manurung Bone Regency. The water distribution data is formulated with a transportation model, so that in order to obtain the model is generated a balance model with addition dummy variable and export table water distribution, obtained a feasible initial solution by calculation using North West Corner method (NWC). Based on a feasible initial solution obtained the optimum solution using the Modified Distribution Method (MODI). The results of this study indicate that with the application of the Transportation Model there was a optimization occurs in water distribution costs in Bone Regency in June 2019 of 52.22% compared to the calculation results by PDAM Wae Manurung Bone Regency.Keywords: Optimization transportation model, north west corner, modified distribution, distribution water.","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126043532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pemodelan Matematika SEIR Penyebaran Penyakit Pneumonia pada Balita dengan Pengaruh Vaksinasi di Kota Makassar","authors":"Syafruddin Side, Wahidah Sanusi, Nurul Aulia Bohari","doi":"10.35580/JMATHCOS.V4I1.20444","DOIUrl":"https://doi.org/10.35580/JMATHCOS.V4I1.20444","url":null,"abstract":"Abstrak. Penelitian ini bertujuan untuk membangun model penyebaran penyakit pneumonia pada balita tipe SEIR (Susceptible- Exposed- Infected- Recovered-), menganalisis model, dan menentukan proporsi minimum vaksinasi. Data yang digunakan adalah data jumlah penderita pneumonia pada balita di Kota Makassar tahun 2019. Hasil penelitian diperoleh model matematika SEIR penyakit pneumonia dalam bentuk sistem persamaan diferensial biasa; titik keseimbangan bebas kecanduan dan titik keseimbangan kecanduan yang keduanya bersifat stabil; bilangan reproduksi dasar untuk simulasi tanpa vaksinasi lebih besar dari 1 yang artinya penyakit masih tetap ada dalam populasi, sedangkan bilangan reproduksi dasar untuk simulasi dengan vasksinasi kurang dari 1 yang artinya penyakit akan menghilang dan tidak meluas dari populasi.Kata Kunci: Titik Ekuilibrium, Bilangan Reproduksi Dasar, Pneumonia, Model SEIR.Abstract.This study aims to build a model of the spread of pneumonia in SEIR (Susceptible-Exposed-Infected-Recovered) toddlers, analyze the model, and determine the minimum proportion of vaccinations. The data used are data on the number of pneumonia sufferers in toddlers in Makassar City in 2019.The results obtained by the SEIR mathematical model of pneumonia in the form of ordinary differential equation systems; addiction free balance points and addiction balance points which are both stable; basic reproduction numbers for simulations without vaccination greater than 1, which means that the disease still exists in the population, while basic reproduction numbers for simulations with vasksination less than 1, which means the disease will disappear and not spread from the population.Keywords: Equilibrium Points, Basic Reproductive Numbers, Pneumonia, SEIR Model.","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124252024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Jumlahan Langsung pada Ring","authors":"Syafruddin Side, Muhammad Abdy, Annisa Uniarti","doi":"10.35580/JMATHCOS.V4I1.20448","DOIUrl":"https://doi.org/10.35580/JMATHCOS.V4I1.20448","url":null,"abstract":"Abstrak. Penelitian ini merupakan penelitian kajian pustaka yang bertujuan untuk mengkaji konsep dasar jumlahan langsung eksternal dan jumlahan langsung internal pada ring beserta sifat-sifatnya. Kajian dimulai dari definisi jumlahan langsung eksternal dan jumlahan langsung internal. Adapun literatur utama yang digunakan adalah buku yang ditulis oleh B. Hartley dan T.O. Hawkes (1970). Hasil yang diperoleh menjelaskan dan menguraikan definisi konsep jumlahan langsung eksternal dan jumlahan langsung internal pada ring, teorema-teorema tentang sifat-sifat jumlahan langsung pada ring yang  memuat masing-masing sebuah teorema akibat dari representasi sifat jumlahan langsung pada S-Near Ring dan jumlahan langsung pada modul yang berkaitan dengan jumlahan langsung eksternal dan jumlahan langsung internal pada ring. Kata Kunci: Ring, Jumlahan Langsung Eksternal, Jumlahan Langsung Internal.Abstract. This research is literature study that aims to examine the basic consept of external direct sum of ring, internal direct sum of ring, and properties of direct sum of ring. The study starts from the definitioan of external direct sum and internal direct sum. The main literature used is a book written by B. Hartley and T.O. Hawkes (1970). The result obtained explain and elaborated on the definitons of external direct sum and internal direct sum of ring, theorems about properties of direct sum of ring that accommodate a theorem resulting from the representation of the properties of direct sum of S-Near Ring and direct sum of modules relating to external rirect sum and internal direct sum of ring.Keywords: Ring, External Direct Sum, Internal Direct Sum.","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129065374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Simulasi Numerik Model Matematika Arus Lalu Lintas Berbasis Fungsi Velositas Underwood","authors":"Muh. Isbar Pratama, Dian Firmayasari, N. Rasyid, H. Harianto","doi":"10.35580/JMATHCOS.V4I1.20445","DOIUrl":"https://doi.org/10.35580/JMATHCOS.V4I1.20445","url":null,"abstract":"Abstrak.Model matematika arus lalu lintas pertama kali dikembangkan oleh Lighthill, Whitham dan Richards pada tahun 1956 yang dikenal dengan model (LWR). Dalam model LWR, fungsi kecepatan adalah unsur yang terpenting. Dalam makalah ini digunakan fungsi kecepatan underwood karena memiliki tingkat kesesuaian yang terbaik dibadingkan dengan fungsi kecepatan lainnya. Metode beda hingga implisit digunakan untuk menemukan solusi numerik model LWR dengan model kecepatan Underwood. Konvergensi metode beda hingga implisit dibuktikan dengan menggunakan teorema Ekuivalensi Lax. Simulasi numerik jalan raya satu lajur sepanjang 10 km dilakukan selama 1 jam menggunakan metode beda hingga implisit berdasarkan data awal dan batas yang dibuat secara artifisial. Simulasi numerik dilakukan dengan dua parameter berbeda. Hasil eksperimen menujukkan bahwa semakin tinggi rata-rata kepadatan kendaraan pada suatu laju mengakibatkan rata-rata kecepatan kendaraan akan berkurang. Kata kunci: Metode Beda Hingga Implisit, Model LWR, Arus Lalu Lintas, Fungsi Felositas Underwood, Simulasi Numerik.Kata kunci : Abstract. Mathematical traffic flow model was first developed by Lighthill, Whitham and Richards in 1956, known as (LWR) model. In LWR model, velocity function was most important. In this paper, Underwood velocity function was used. Implicit finite difference method used to found the numerical solution of LWR model with Underwood velocity model. Convergence the implicit finite difference method proved using the Lax equivalence theorem. The numerical simulation of 10 km highway of single lane was performed for 1 hours using the implicit finite difference method based on artificially generated initial and boundary data. Numerical simulation performed with two different parameters. An experimental result for the stability condition of the numerical scheme was also presented. Density, velocity, and fluks for 1 hours was experimental result of numerical simulation.Keywords: Implicit finite difference method, Lax equivalence theorem, LWR model, Traffic flow, Under-wood velocity Function, Numerical simulation.","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129280063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pemodelan Matematika SEIRS Pada Penyebaran Penyakit Malaria di Kabupaten Mimika","authors":"Hisyam Ihsan, Syafruddin Side, Musdalifa Pagga","doi":"10.35580/JMATHCOS.V4I1.20446","DOIUrl":"https://doi.org/10.35580/JMATHCOS.V4I1.20446","url":null,"abstract":"Abstrak. Penelitian ini  bertujuan untuk membangun model penyebaran pada penyakit malaria tipe SEIRS (Susceptible-Exposed- Infected- Recovered- Susceptible) dengan menambahkan parameter penanganan(pengobatan) pada kelas Exposed dan asumsi bahwa manusia yang pulih dapat rentan kembali terkena penyakit malaria. Model ini dibagi menjadi empat kelas yaitu, rentan, terinfeksi tapi belum aktif, terinfeksi, dan sembuh. Data yang digunakan adalah data jumlah penderita penyakit malaria dari Dinas Kesehatan Kabupaten Mimika tahun 2018. Model matematika tipe SEIRS digunakan untuk menentukan titik equilibrium. Berdasarkan hasil simulasi dari model SEIRS diperoleh bilangan reproduksi dasar  sebesar 0,09 yang menandakan bahwa penyebaran penyakit malaria tidak menyebabkan orang lain terkena penyakit malaria.Kata Kunci: Titik Equilibrium, Bilangan Reproduksi Dasar, Malaria, Model SEIRSAbstract. This research aims to build a model of the spread of malaria diseases type SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) by adding treatment parameters (treatment) in the Exposed class and the assumption that humans who recover can be vulnerable to malaria again. This model is divided into four classes namely, vulnerable, infected but not yet active, infected, and cured. The data used are data on the number of malaria sufferers from the Mimika District Health Office in 2018. The mathematical model of the type SEIRS is used to determine the equilibrium point. Based on the simulation results of the SEIRS model, the basic reproduction number (R0) of 0.09 indicates that the spread of malaria does not cause others to contract malaria.Keywords: Equilibrium Point, Basic Reproductive Numbers, Malaria, SEIRS Model","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116334936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solusi Persamaan Schrodinger dengan Menggunakan Metode Transformasi Diferensial","authors":"Muhammad Abdy, Hisyam Ihsan, Dhea Ayu Rossyana Dewi","doi":"10.35580/JMATHCOS.V4I1.20449","DOIUrl":"https://doi.org/10.35580/JMATHCOS.V4I1.20449","url":null,"abstract":"Abstrak. Penelitian ini membahas tentang solusi persamaan diferensial parsial linier yaitu persamaan Schrodinger. Solusi persamaan ini dilakukan dengan menggunakan metode transformasi diferensial yang merupakan metode semi-numerik-analitik yang dapat digunakan untuk menyelesaikan persamaan diferensial biasa ataupun persamaan diferensial parsial linier dan nonlinier. Metode transformasi diferensial merupakan metode yang menggunakan teori ekspansi deret pangkat pada bentuk transformasinya untuk menentukan solusi. Pada penelitian ini digunakan dua nilai awal pada persamaan Schrodinger yang diberikan. Solusi dengan kedua nilai awal yang diberikan diperoleh dengan menggunakan ekspansi deret Maclaurin. Kemudian solusi tersebut disimulasikan menggunakan software Maple18. Akibatnya, metode transformasi diferensial pada penelitian ini merupakan salah satu metode yang mampu menghasilkan solusi untuk persamaan Schrodinger..Kata Kunci: Persamaan Schrodinger, Metode Transformasi DiferensialAbstract. This study discusses the solution of linear partial differential equations, namely Schrodinger equation. The solution of the equation is done by using the differential transformation method which is a semi-numerical-analytical method, it can be used to solve both ordinary differential equations and linear or nonlinear partial differential equations. Differential transformation method is a method uses the theory of rank expansion in the form of transformation to determine solutions. In this study, two initial values in the given Schrodinger equation were used. Solutions with both initial values given are obtained using the Maclaurin series expansion. Then, the solution is simulated using Maple18 software. As a result, the differential transformation method in this study is one method that is able to solve a solution to the Schrodinger equation.Keywords: Schrodinger Equation, Differential Transformation Method","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121626215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dual Reciprocity Boundary Element Method untuk Menyelesaikan Masalah Infiltrasi Stasioner pada Saluran Datar Periodik","authors":"M. Megasari","doi":"10.35580/JMATHCOS.V4I1.20447","DOIUrl":"https://doi.org/10.35580/JMATHCOS.V4I1.20447","url":null,"abstract":"Abstrak. Penelitian ini membahas tentang penyelesaian masalah infiltrasi stasioner dari saluran datar dengan Dual Reciprocity Boundary Element Method (DRBEM). Persamaan pembangun untuk masalah ini adalah persamaan Richard. Menggunakan transformasi Kirchhoff dan relasi eksponensial konduktifitas hidrolik, persamaan Richard ditransformasi ke dalam persamaan infiltrasi stasioner dalam Matric Flux Potential (MFP). Persamaan infiltrasi dalam MFP selanjutnya diubah ke dalam persamaan Helmholtz termodifikasi. Model matematika infiltrasi stasioner pada saluran datar berbentuk Masalah Syarat batas Helmholtz termodifikasi Solusi numerik diperoleh dengan menyelesaikan persamaan Helmholtz termodifikasi menggunakan Dual Reciprocity Boundary Element Method (DRBEM) dengan pengambilan jumlah titik kolokasi eksterior dan interior yang bervariasi. Lebih lanjut, solusi numerik dan solusi analitik dibandingkan..Kata Kunci: Infiltrasi, saluran datar, persamaan helmholtz termodifikasi, DRBEM.Abstract. This research discusses about the problem solving of steady infiltration problem from flat channel with Dual Reciprocity Boundary Element Method (DRBEM). The governing equation for this problem is Richard’s equation. Using Kirchhoff transformation and exponential hydraulic conductivity relation, Richard’s equation is transformed into steady infiltration equation in the form of MFP. Infiltration equation in the form of MFP is then transformed to modified Helmholtz equation. A mathematical model of steady infiltration from flat channel in the form of boundary condition problem of modified Helmholtz EQUATION. Numerical solution is obtained by solving modified Helmholtz equation by using Dual Reciprocity Boundary Element Method (DRBEM) with various number of exterior and interior collocation points. Moreover, numerical and analytic solution are then compared.Keywords: infiltration, flat channel, modified Helmholtz equation, DRBEM","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121782242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}