Numerical Modeling of Oil Palm Plantation Area Growth in Indonesia Using Verhulst Model

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Authors

  • Ajril Abyad Al Haq Universitas PGRI Ronggolawe
  • Muna Afdi Muniroh Universitas PGRI Ronggolawe

DOI:

https://doi.org/10.32665/james.v9i2.6337

Keywords:

Backward Differentiation Formula, Milne Method, Oil Palm Plantation, Runge-Kutta Method, Verhulst Model

Abstract

The expansion of oil palm plantation area in Indonesia exhibits nonlinear growth behavior influenced by environmental, spatial, and policy constraints. This study aims to model the growth of oil palm plantation area using the Verhulst (logistic) growth model and to obtain numerical solutions of the resulting nonlinear differential equation. A quantitative approach is employed, in which the fourth-order Runge–Kutta (RK4) method is used to generate the required initial values, followed by two predictor–corrector schemes, namely the Adams–Bashforth–Backward Differentiation Formula (AB4–BDF4) and the Milne–Backward Differentiation Formula (Milne–BDF4), which are compared to approximate the long-term growth dynamics. The analysis utilizes annual oil palm plantation area data from 2017 to 2024 obtained from Statistics Indonesia (BPS). Numerical results indicate that all methods produce stable solutions, with relative errors remaining bounded and non-divergent throughout the simulation, on the order of 10-6. On average, the AB4–BDF4 scheme yields a relative error of 3.2477330 × 10-6, compared to 5.9206896 × 10-6 for the Milne–BDF4 scheme, corresponding to an accuracy improvement of approximately 1.8 times. The estimated intrinsic growth rate is r≈0.15, and the estimated carrying capacity is 20 million hectares, representing the maximum sustainable oil palm plantation area under current growth trends.

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Published

2026-07-30

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Vol. 9 No. 2 (2026): Journal of Mathematics Education and Science

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Abstract View: 41, PDF Download: 17