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All Journal Epsilon: Jurnal Matematika Murni dan Terapan
Faisal Faisal
Program Studi Matematika FMIPA Universitas Lambung Mangkurat
Decision Sciences, Operations Research & Management Transportation

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ESTIMASI PARAMETER MODEL LOGISTIK DAN RICHARDS PADA PRODUKSI PADI: STUDI KASUS KALIMANTAN SELATAN Yuni Yulida; Faisal Faisal; Muhammad Ahsar Karim; Abdul Hadi; Noorul Wakhdah; Tiara Amaliya
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.16648

Abstract

Padi (Oryza sativa) merupakan komoditas pangan strategis di Indonesia karena beras menjadi sumber karbohidrat utama masyarakat dan berperan penting dalam menjaga ketahanan pangan nasional, termasuk di Kalimantan Selatan yang menjadi salah satu daerah produsen utama. Penelitian ini bertujuan mengestimasi parameter dan membandingkan kinerja model logistik dan Richards dalam memodelkan serta memproyeksikan produksi padi berdasarkan data historis dari Badan Pusat Statistik. Estimasi parameter dilakukan dengan metode nonlinear least squares, sedangkan akurasi model dievaluasi dengan Mean Absolute Percentage Error (MAPE). Hasil penelitian menunjukkan bahwa kedua model mampu merepresentasikan pola pertumbuhan sigmoidal produksi padi, dengan model Richards memberikan hasil yang lebih akurat (MAPE <15%) dibandingkan model logistik. Selain itu, analisis data luas panen mengindikasikan adanya penurunan signifikan sejak 2018, dengan kehilangan kumulatif sekitar 3,54 juta hektar pada periode 2003–2024 dan rata-rata penurunan tahunan sebesar 161 ribu hektar, yang diduga dipengaruhi alih fungsi lahan serta bencana banjir. Proyeksi skenario optimis menunjukkan adanya potensi peningkatan produksi, sedangkan skenario pesimis memperlihatkan kecenderungan stagnasi akibat keterbatasan lahan dan tekanan eksternal lainnya. Dengan demikian, model Richards dinilai lebih representatif dalam memproyeksikan produksi padi di Kalimantan Selatan, dan hasil penelitian ini dapat menjadi dasar dalam perumusan kebijakan perlindungan serta rehabilitasi lahan pertanian guna mendukung ketahanan pangan berkelanjutan.
NON-STANDARD SCHEME DISCRETIZATION (NSFD) FOR COMMENSALISM SYMBIOSIS MODEL WITH HARVESTING IN COMMENSAL POPULATIONS Nurmaini Puspitasari; Faisal Faisal; Yuni Yulida; Nur Wahidiyatil Jannah; Muhammad Afief Balya
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.16551

Abstract

Dynamic analysis on the model of commensalism symbiosis with the discretized Michaelis-Menten cropping by using different schemes to non-standard finite difference (NSFD) is the main focus in this article. The analysis is started by searching the equilibrium points with their existence terms and local stability with their stability terms. In this article, there are four equilibrium points. The points are the extinction point of both populations, the host extinction point, the commensal extinction point, and the point where both populations can coexist (the coexistence equilibrium point). The existence of a host extinction point and a point at which both populations can coexist depends on the conditions of existence that must be met. Among the four equilibrium points, the commensal extinction point and the coexistence equilibrium point are locally asymptotically stable provided that the specified stability conditions are met. In the final analysis, numerical simulations were performed using the 4th order Runge–Kutta scheme for the continuous model and the NSFD scheme for the discrete model. The results show that the NSFD scheme offers greater flexibility in choosing the integration time step to ensure convergence to a feasible solution, outperforming the 4th order Runge–Kutta scheme in this respect.
Co-Authors Abdul Hadi Muhammad Afief Balya Muhammad Ahsar Karim Noorul Wakhdah Nur Wahidiyatil Jannah Nurmaini Puspitasari Tiara Amaliya Yuni Yulida