PENERAPAN METODE RUNGE KUTTA FEHLBERG PADA PERSAMAAN LOGISTIK DALAM MEMPREDIKSI PERTUMBUHAN PENDUDUK DI SULBAR
Application Of The Runge Kutta Fehlberg Method In Logistic Equations in Predicting Population Growth in Sulbar
DOI:
https://doi.org/10.59896/aqlu.v2i2.99Keywords:
Ordinary differential equations, runge kutta fehlberg 45 method, logistics equation, population growthAbstract
This research discusses the application of the Runge Kutta Fehlberg method in predicting population growth in West Sulawesi through the logistic equation. Employing applied research methodology, the study seeks to forecast future population trends in the West Sulawesi province. Utilizing a step size of h = 0.01 and a growth rate of m = 0.0198, the Runge-Kutta Fehlberg method (RKF 45) was applied, starting from an initial population value of P (t0) = 1.419.229 individuals, resulting in a projected population of P (t10) = 1.506.142 individuals. These findings demonstrate the applicability of the Runge-Kutta Fehlberg (RKF 45) method in predicting population dynamics in West Sulawesi Province.
References
Atmika Ketut Adi. (2016). Metode Numerik. Univeritas Udayana: Diktat.
Baiduri. (2002). Persamaan Diferensial dan Matematika Model. Malang: UMM Press.
Butcher, C. J. (2008). Numerical Methods for Ordinary Differential Equations. England: JohnWiley & Suns Ltd.
Chapra, Steven C dan Canale, Raymond P. (2002). Numerical Methods For Engineers with software and programming applications. Fourth Edition. New York: The Mc Graw-Hill Companies, Inc.
Djojodihardjo, H. (2000). Metode Numerik. Jakarta: Gramedia Pustaka Utama.
Dwi, Septika Haryati. (2022). Statistik Daerah Provinsi Sulawesi Barat 2022. Mamuju: Badan Pusat Statistik Provinsi Sulawesi Barat.
Eziokwu, C. Emmanuel, dkk. (2020). On Review of the Convergence Analyses of the Runge Kutta Fixed Point Iterative Methods. Asian Journal of Pure and Applied Mathemtics. Vol.2 No.1.
Kurnia , Yenni. (2023). Provinsi Sulawesi Barat Dalam Angka 2023. Mamuju: Badan Pusat Statistik Provinsi Sulawesi Barat.
Kusuma Jeffry & Abdillah. (2010). Solusi Numerik Persamaan Diferensial Biasa Dengan Metode Adams-Bashforth-Moulton Orde Lima. Jurnal Matematika, Statistika,& Komputasi,Volume 7 nomor 2.
Latip Faranika, Dorrah Azis, & Suharsono. (2017). Perbandingan Metode Adams Bashforth-Moulton dan Metode Milne-Simpson Dalam Penyelesaian Persamaan Diferensial Euler Orde 8. Universitas Lampung: Prosiding Nasional Metode Kuantitatif.
Maharani, Swasti dan Edy Suprapto. (2018). Analisis Numerik. Magetan: CV. AE MEDIA GRAFIKA.
Mardianto, Y. B. (2022). Metode Runge-Kutta Orde 4 Dalam Penyelesaian Persamaan Gelombang 1D Syarat Batas Dirichlet. Indonesian Journal of Applied Mathematics Vol 2.
Mathews, & Kurtis. (2004) . Numerical Method Using Matlab. 4th Editions. New Jersey: The Pretince Hall, Inc.
Munir, R. (2003). Metode Numerik. Jakarta: Informatika.
Nugoroho Didit. (2010). Persamaan Diferensial Biasa dan Aplikasinya. Yogyakarta: Graha Ilmu.
Nurmadhani Nadya, & Faisol. (2022). Penerapan Model Pertumbuhan Logistik Dalam Memproyeksikan Jumlah Penduduk di Kabupaten Sumenep. Jurnal Edukasi Dan Sains Matematika, Volume 8 nomor 2.
Pratiwi, C. D. (2020). Aplikasi Persamaan Diferensial Model Populasi Logistik untuk Mengestimasi Penduduk di Kota Balikpapan. AdMathEdu, Volume 10 no 1.
Redjeki, Sri P. (2010). Persamaan Diferensial. Bandung: Diktak Kuliah MA2271 Metode Matematika.
Richard L. Burden & J. Douglas Faires. (2011). Numerical Analysis. California: Cengage Learning.s
Ritschel, T. (2013). Numerical Methods for Solution of Differential Equations. Lyngby: Departement of Applied Mathematics and Computer Science.
Sasongko, S. (2010). Metode Numerik dengan Scilab. Yogyakarta: ANDI Yogyakarta.
Tang, P., & Tay, E. (2021). Penerapan Model Logistik Eksponensial dan Model Logistik untuk Proyeksi Penduduk Tahun 2024 di Kabupaten Alor. SAINSTEK, Volume 5 nomor 1.
Triatmodjo Bambang. (2022). Metode Numerik. Yogyakarta: Beta Offset.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Syarfiah Syarfiah, Muh. Irwan, Sri Dewi Anugrawati
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
