Penerapan Metode Adams Bashforth-Moulton dan Runge-Kutta dalam Memprediksi Pertumbuhan Penduduk di Sumatera Utara pada Tahun 2029 Berdasarkan Data Jumlah Penduduk pada Tahun 2015-2024

Abstract

The ABM5 method is a predictor and corrector (multistep) method in solving non-linear ordinary differential equations that utilizes the value of several previous periods to calculate the current value and future values, one of which is the RK5 method. The logistic equation is a non-linear ordinary differential equation that describes population growth. This study aims to apply the fifth-order Adams Bashforth-Moulton method (ABM5) and fifth-order Runge-Kutta method (RK5) in predicting population growth in North Sumatra Province in 2029 based on population data in 2015-2024 using a logistic equation model. The research results of the RK5 method showed the prediction of population in 2015-2019 and ABM5 showed the prediction of pupulation in 2020- 2029 using five initial values of prediction from RK5. Based on the calculation results, the numerical solution of the logistic equations for population growth in 2025 to 2029 with step size h = 1, the carrying capacity of North Sumatra Province K = 70.000.000 and the growth rate r = 0,014 is 16.254.908 people with an average growth rate of 165,508 people per year.