Articles
<![CDATA[Model Matematika Vibrasi Dawai Dikenai Massa yang Berjalan di Atasnya ]]>
<![CDATA[Miftakul Janah]]>;
<![CDATA[Ari Kusumastuti]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 1, No 4 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v1i4.14446
<![CDATA[This study discusses the formulation of a mathematical model of string vibration when subjected to mass. There are two variables resulting from the formulation of the model, namely the deflection of the string and the angle of the string . The deflection of the string and the angle of the string . are affected by the friction force, tension force, spring force, and gravity. Then the identification of the working potential and kinetic energy is carried out to obtain the Lagrange equation of the deflection and angle of the string. Based on the formulation steps that have been described, the mathematical model obtained is an ordinary differential equation of the order of one to the power of two. Furthermore, the model is calculated numerically by assigning values to the parameters involved. So it is known that with a string mass of 0.005 kg, 0.05 kg, 0.5 kg, a string mass of 0.075 kg, and an object radius of 0.07 m, it is known that the deflection of the string is greater if the object's mass is greater. While the angle of the string is in a state of equilibrium before being subjected to a mass and experiencing vibration after being subjected to a mass.]]>
<![CDATA[Metode Backward Time Central Space dalam Penyelesaian Model Matematika Vibrasi Dawai pada Alat Musik Petik ]]>
<![CDATA[Atik Damayanti]]>;
<![CDATA[Ari Kusumastuti]]>;
<![CDATA[Nurul A. Hidayati]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 1, No 4 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v1i4.14454
<![CDATA[This research was conducted to obtain a numerical solution of the mathematical model of string vibration on stringed instruments. This mathematical model is a representation of the phenomenon of string vibration on a stringed instrument subject to deviation. The model was constructed by Kusumastuti, et al (2017) and is in the form of a second-order partial differential equation. The method used in completing this research is the BTCS (Backward Time Central Space) method. The numerical solution is obtained by the following steps, 1). Discretize mathematical models, as well as discretize initial conditions and boundary conditions. 2). Performing stability analysis of numerical solutions to determine the terms of solution stability and conducting consistency analysis as a condition of the convergence of the obtained numerical solutions. 3). Simulate numerical solutions and perform graph interpretations. The results show that the numerical solution of the mathematical model of string vibration on stringed instruments is unconditionally stable and has an error order (〖∆x〗^2,〖∆t〗^3).]]>
<![CDATA[Analisis Dinamik Model Matematika Penyebaran COVID-19 Pada Populasi SEIR ]]>
<![CDATA[Ester Meyliana]]>;
<![CDATA[Ari Kusumastuti]]>;
<![CDATA[Juhari Juhari]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 1, No 4 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v1i4.14458
<![CDATA[This study discusses the dynamic analysis of the mathematical model of the spread of COVID-19 using daily cases in Indonesia which are classified into four variables, namely, Susceptible (S), Exposed (E), Infected (I), and Recovered (R) which are then analyzed dynamically by calculate the equilibrium point and look for stability properties. The two equilibrium points of this model are the disease-free equilibrium point and the endemic equilibrium point . Then, it is linearized around the equilibrium point using the given parameters. Linearization around the equilibrium point produces four eigenvalues, one of which is positive. Linearization around the equilibrium point yields two negative real eigenvalues and a pair of complex eigenvalues with negative real parts. Phase portraits and numerical simulations have shown that all variables S, E, I, and R will be asymptotically stable locally towards the equilibrium point, namely the endemic equilibrium point . Thus, based on the dynamic analysis obtained, it is shown that the disease-free equilibrium point is unstable and the endemic equilibrium point is locally asymptotically stable.]]>
<![CDATA[Simulasi Numerik Model Matematika Vibrasi Dawai Flying Fox Menggunakan Metode Adams-Bashforth-Moulton ]]>
<![CDATA[Febry Noorfitriana Utami]]>;
<![CDATA[Ari Kusumastuti]]>;
<![CDATA[Juhari Juhari]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 2, No 1 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v2i1.14512
<![CDATA[This study discusses numerical simulation using the Adams-Bashforth-Moulton (ABM) method of order 4 in the flying fox string mathematical model which is in the form of ordinary differential equations depending on time, consisting of two equations, namely the equation of the flying fox string y(t) and the angular equation of the flying fox string θ(t). This mathematical model is a model that has been constructed by Kusumastuti, et al (2017) and has been validated by comparing analytical solutions to its numerical solutions by Sari (2018). The analysis of the behavior of the Kusumastuti 2017 model conducted by Makfiroh (2020) shows that the phase portrait graph is in the form of a spiral with eigenvectors pointing towards the equilibrium point so that the mathematical model of the flying fox string vibration can be concluded as a valid mathematical model that is close to the actual situation. This study attempts to determine the numerical simulation of the deflection of the flying fox string y(t) and the numerical simulation of the angle of the flying fox string θ(t). The Runge-Kutta method of order 4 was used to generate 3 initial values for order 4 ABM. Next, a comparison of the y(t) and θ(t) solution graphs of order 4 ABM with the solution graph with Runge-Kutta of order 4 was performed in Sari 2018. The first simulation was carried out when h=1, the difference in the value of y(t) of order 4 ABM and Runge-Kutta order 4 fluctuated in the range of [0,0.09] with almost the same graphic profile, and the difference in the value of θ(t) ABM of order 4, and Runge-Kuta order 4 which is quite large with different graphic profiles. The second simulation was carried out when h=0.01, the difference in the value of y(t) of order 4 ABM and Runge-Kutta order 4 was fluctuating which also ranged from [0.0.09] with the same graphic profile, and the difference in the values of θ(t) ABM of order 4 and Runge -Kutta order 4 fluctuates in the range of [0,1] with the same graphic profile. So concluded that when h=0.01 comparison of ABM of order 4 and Runge-Kutta of order 4 is the best for displaying the graph profiles of y(t) and θ(t). Further research can explore numerical solutions using other methods.]]>
<![CDATA[Implementasi Jaringan Syaraf Tiruan Backpropagation untuk Menentukan Prediksi Jumlah Permintaan Produksi Dodol Apel ]]>
<![CDATA[Farrah Nurmalia Sari]]>;
<![CDATA[Ari Kusumastuti]]>;
<![CDATA[hisyam Fahmi]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 2, No 2 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v2i2.14899
<![CDATA[Forecasting is importantly in accordance with the planning strategy; therefore it will affect the way of decision making. One of the forecasting methods is Artificial Neural Network with Backpropagation as the algorithm. This research aims to measure the accuracy of the network architecture which is being applied in order to calculate the prediction of the future’s apple paste product monthly demand which was obtained from CV. Bagus Agriseta Mandiri. The data which are being used are 36 monthly data from the year 2017, 2018 and 2019. Furthermore, the data obtained are normalized and divided into two, 66,66% as the data for training process and 33,33% as the data for testing process. Network architecture that is applied in this research is 12 : 10 :1, where 12 are neurons for input layer, 10 are neurons for one hidden layer and 1 is neuron for output layer. The Network with that framework obtained a result 20.161% for MAPE and 79.839% for the accuracy. That model is categorized as good enough for its forecasting ability. Moreover, the network was entirely validated using k-fold cross validation method with . The result obtained as follows: the average of MAPE is 47.079% and the average accuracy is 52.921%. According to it, the entire model can be categorized as good enough in order to run a forecast. As a comparison, another testing has been done with the same fold but different in the network architecture (model 6 – 8 – 1). The second model obtained results as follows: the average of MAPE is 26.74% and the average accuracy is 73.18%, so that the two prediction models’ ability are in the same category, it is good enough to run a forecast.]]>
<![CDATA[Analisis Dinamik Model Infeksi Mikrobakterium Tuberkulosis Dengan Dua Lokasi Pengobatan ]]>
<![CDATA[Ummul Aulia KT]]>;
<![CDATA[Heni Widayani]]>;
<![CDATA[Ari Kusumastuti]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 2, No 3 (2023): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v2i3.16753
<![CDATA[Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis. The disease is considered dangerous because it infects the lungs and other organs of the body and can lead to death. This study discusses a mathematical model for the spread of tuberculosis with two treatment sites as an effort to reduce the transmission rate of TB cases. Treatment for TB patients can be done at home and in hospitals. The purpose of this study was to construct a mathematical model and analyze the qualitative behavior of the TB spread model. The construction of the model uses the SEIR epidemic model which is divided into five subpopulations, namely susceptible subpopulations, latent subpopulations, infected subpopulations receiving treatment at home, and infected subpopulations receiving treatment at the hospital, and cured subpopulations. The analysis of qualitative behavior in the model includes determining the local and global equilibrium and stability points. The results of the analysis shows that the model has two equilibrium points, namely a disease-free equilibrium point and the endemic equilibrium point. The existence of endemic equilibrium point and the local and global stability of the two equilibrium points depend on the basic reproduction number denoted by . If , there is only disease-free equilibrium point. If , there are two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. Stability analysis shows that the disease-free equilibrium point is locally and globally asymptotically stable if . While, if , the endemic equilibrium point will be asymptotically stable locally and globally.]]>
<![CDATA[Penyelesaian Sistem Persamaan Hukum Laju Reaksi dengan Metode Transformasi Differensial ]]>
<![CDATA[Siti Maftuhah]]>;
<![CDATA[Heni Widayani]]>;
<![CDATA[Ari Kusumastuti]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 2, No 4 (2023): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v2i4.16805
<![CDATA[This research is focused on solving the rate law equation by using the differential transformation method. The rate law equation describes the chemical reaction problem from the concentration of a reactant that produces a product. The differential transformation method is a semi-analytic numerical method that can provide approximate solutions in the form of a series because the method is obtained from the expansion of the Taylor series expansion. With the help of Maple software, a comparison of the solution plots of y_1 (t),y_2 (t) and y_3 (t), can be observed that the difference in computational results between the Runge-kutta method and the differential transformation depends on the order of k. The curve of the differential transformation method is getting closer to the curve of the Runge-Kutta method at a certain value of k for each y_1 (t),y_2 (t) and y_3 (t). The conclusion of this research is that the application of the differential transformation method has been successfully carried out in the case of a system of ordinary differential equations. For further research, the researcher suggests that the next research applies the method of differential transformation in cases and initial values that are more varied.]]>
<![CDATA[Analisis Model Epidemi SEIR Menggunakan Metode Runge-Kutta Orde 4 pada Penyebaran COVID-19 di Indonesia ]]>
<![CDATA[Rahmadhani, Anis Putri]]>;
<![CDATA[Kusumastuti, Ari]]>;
<![CDATA[Juhari, Juhari]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 2, No 3 (2023): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v2i3.16355
<![CDATA[This study discusses the analysis of the Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model using the fourth-order Runge-Kutta method on the spread of COVID-19 in Indonesia by taking into account the factors limiting community interaction and the percentage of vaccination as model parameters. The purpose of this study was to determine the application of the Susceptible–Exposed–Infected–Recovered (SEIR) model using the fourth-order Runge-Kutta method in dealing with COVID-19 in Indonesia. The steps in analyzing the model are to determine the stability of the model that produces local asymptotic stability, then carry out the implementation as well as simulation using the fourth-order Runge-Kuta method in dealing with COVID-19 in Indonesia. The calculation results show the effect of limiting community interaction and vaccination in reducing cases of COVID-19 infection. Where, when limiting public interaction, the number of cases of COVID-19 infection is lower than before the restrictions on community interaction were carried out, and the higher percentage of vaccinations also resulted in more sloping infection cases. This study provides information that if restrictions on community interaction continue to be carried out by continuing to increase the percentage of vaccinations, it is estimated that the daily graph of positive cases of COVID-19 will be increasingly sloping and close to zero. Thus, the addition of new cases will decrease and it is hoped that the COVID-19 pandemic will end soon.]]>
<![CDATA[Solusi Numerik Model Gerak Osilasi Vertikal dan Torsional Pada Jembatan Gantung ]]>
<![CDATA[Permata, Hendrik Widya]]>;
<![CDATA[Kusumastuti, Ari]]>;
<![CDATA[Juhari, Juhari]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 1, No 1 (2021): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v1i1.13409
<![CDATA[Model gerak osilasi vertikal dan torsional merupakan model yang menggambarkan gerak osilasi vertikal dan gerak torsional pada batang yang digantung. Gerak osilasi vertikal merupakan gerak naik turun suatu benda yang terjadi terus berulang, dan kemudian pada waktu tertentu akan berhenti atau mengalami redaman. Gerak torsional merupakan getaran sudut dari suatu objek yang mengalami rotasi. Model gerak osilasi dan torsional pada dasarnya merupakan sistem persamaan diferensial orde dua. Tujuan dari penelitian ini adalah untuk mengetahui solusi numerik model gerak osilasi vertikal dan torsional menggunakan metode Adams-Bashforth-Moulton orde empat, lima, dan enam. Model gerak osilasi vertikal dan torsional terlebih dahulu diselesaikan menggunakaan metode Runge-Kutta-Fehlberg orde lima untuk mendapatkan solusi awal kemudian model tersebut diselesaikan menggunakan metode Adams-Bashforth-Moulton orde empat, lima dan enam. Hasil solusi numerik setiap metode Adam-Bashforth-Moulton selanjutnya diuji dengan galat relatif. Hasil simulasi numerik model gerak osilasi vertikal dan torsi diperoleh bahwa gerak osilasi vertikal dan gerak torsional merupakan gerak harmonik teredam dan semakin tinggi orde pada metode Adams-Bashforth-Moulton maka akan lebih cepat galat relatif menuju nilai nol dan sebaliknya]]>
<![CDATA[Model Epidemi Suspected Exposed Infected Recovered (SEIR) Pada Penyebaran COVID-19 Orde-Fraksional ]]>
<![CDATA[Nisa, Khoirotun]]>;
<![CDATA[Rahman, Hairur]]>;
<![CDATA[Kusumastuti, Ari]]>
<![CDATA[ Jurnal Riset Mahasiswa Matematika Vol 1, No 3 (2022): Jurnal Riset Mahasiswa Matematika ]]>
Publisher : <![CDATA[Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang ]]>
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DOI: 10.18860/jrmm.v1i3.14440
<![CDATA[This article discusses the solution to the fractional order SEIR equation with the help of the Homotopy Perturbation Method (HPM). This mathematical model is the SEIR model of the spread of COVID-19 cases in Indonesia. In general, the nonlinear Ordinary Differential Equation System (ODES) solution is quite difficult to solve analytically, so this research will transform the nonlinear ODES into a Fractional Differential Equation System (FDES). The method used in completing this research is the HPM method. The solution for the fractional order by the HPM method is obtained by the following steps: 1). Multiply each SEIR equation against the embedding parameter and equate each coefficient in the assumed infinite series to find the solution, 2). Simulate numerical solutions and perform graph interpretation. The numerical simulation shows that the susceptible human population, the infected human population without symptoms, the recovered human population has increased, in contrast to the infected human population with decreased symptoms. The HPM method in its numerical solution shows a fairly small comparison to the nonlinear ODES solution.]]>
