Analisis Simulasi Solusi Numerik Model Lotka-Volterra dengan Metode Runge-Kutta-Fehlberg (Studi Kasus Populasi Musang Luwak (Paradoxurus hermaphroditus) dan Ayam Hutan Merah (Gallus gallus) di Taman Nasional Alas Purwo)

Randhi Nanang Darmawan; Rachmaniah Mirza Hariastuti

doi:10.15575/kubik.v3i2.4112

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Randhi Nanang Darmawan
Universitas PGRI Banyuwangi
Indonesia

Rachmaniah Mirza Hariastuti
Universitas PGRI Banyuwangi
Indonesia

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Analisis Simulasi Solusi Numerik Model Lotka-Volterra dengan Metode Runge-Kutta-Fehlberg (Studi Kasus Populasi Musang Luwak (Paradoxurus hermaphroditus) dan Ayam Hutan Merah (Gallus gallus) di Taman Nasional Alas Purwo)

Randhi Nanang Darmawan^(1*), Rachmaniah Mirza Hariastuti⁽²⁾

(1) Universitas PGRI Banyuwangi, Indonesia
(2) Universitas PGRI Banyuwangi, Indonesia
(*) Corresponding Author

Abstract

Model mangsa-pemangsa, atau biasa disebut dengan model Lotka-Volterra adalah suatu model dalam bentuk sistem persamaan diferensial biasa non-linier yang menggambarkan interaksi antara dua makhluk hidup yang berhubungan dalam bentuk predasi. Sehingga untuk menyelesaikan model tersebut harus menggunakan metode numerik yaitu metode Runge-Kutta-Fehlberg (RKF45), dikarenakan model tersebut berupa sistem persamaan diferensial non-linier yang mana sulit untuk menentukan solusi analitik, solusi dari sistem persamaan diferensial tersebut adalah berupa profil interaksi antara antara kedua spesies yang saling memangsa dalam suatu ekosistem. Dalam artikel ini, peniliti mengambil studi kasus populasi Musang Luwak (Paradoxurus hermaphroditus) dan Ayam Hutan Merah (Gallus gallus) yang hidup di Taman Nasional Alas Purwo, yang mana keduanya memiliki hubungan predasi. Hasil dari artikel ini adalah profil simulasi model Lotka-Volterra antara kedua spesies dengan melakukan beberapa variasi parameter-parameter sehingga hasil akhirnya adalah suatu profil yang dapat menggambarakan kondisi yang memungkinkan kepunahan antara masing-masing spesies.

Keywords

Lotka-Volterra; Predator-Prey; Runge-Kutta-Fehlberg; Sistem Persamaan Diferensial.

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References

Angga, T. F., 2010. Penerapan Model Mangsa-Pemangsa Lotka-Volterra (Studi Kasus Perkebunan Kopi, Kakao (PTPN X), dan Kelapa Rakyat di Jember), Jember: FMIPA Universitas Jember: Tidak Dipublikasikan.Skripsi.

Anisiu, M. C., 2014. Lotka, Volterra and their Model. Didactica Mathematica , Volume 32, pp. 9-17.

Campbel, S. L. & Haberman, S., 2008. Introduction to Differential Equations with Dynamical System. New Jersey: Pricenton University Press.

Chapra, S. C. & Canale, R. P., 2010. Numerical Method for Engineers. Sixth ed. New York: McGraw-Hill.

Boyce, W. E. & DiPrima, R. C., 2008. Elementary Differential Equations and Boundary Value Problem. Ninth ed. New York: John Willey & Sons.

DOI: https://doi.org/10.15575/kubik.v3i2.4112

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Analisis Simulasi Solusi Numerik Model Lotka-Volterra dengan Metode Runge-Kutta-Fehlberg (Studi Kasus Populasi Musang Luwak (Paradoxurus hermaphroditus) dan Ayam Hutan Merah (Gallus gallus) di Taman Nasional Alas Purwo)

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