Analisis Akurasi Dan Waktu Komputasi Metode Runge-Kutta Pada Persamaan Diferensial Linear Orde Satu
DOI:
https://doi.org/10.21154/imej.v2i1.47Keywords:
akurasi, simulasi numerik, Runge-Kutta, persamaan diferensial linear orde satu, waktu komputasiAbstract
Tidak semua persamaan diferensial dapat diselesaikan secara analitik. Untuk mengatasi hal ini dapat digunakan solusi pendekatan menggunakan metode numerik, seperti metode Runge-Kutta. Penelitian ini menyelidiki konsistensi lima variasi metode Runge-Kutta (Euler, Heun, Ralston, RK3, dan RK4) dalam menyelesaikan persamaan diferensial linear orde satu. Persamaan yang digunakan mencakup model pertumbuhan eksponensial dan model pendinginan Newton. Hasil simulasi menunjukkan bahwa semua metode menghasilkan solusi numerik mendekati solusi eksak. Berdasarkan perhitungan galat, metode Euler memiliki galat maksimum tertinggi, sementara RK4 paling akurat. Dari segi efisiensi, metode Euler menunjukkan waktu komputasi tercepat, sedangkan RK4 paling lambat. Meskipun Heun dan Ralston sama-sama metode orde dua, metode Heun lebih efisien karena formulanya lebih sederhana dibandingkan Ralston.
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