Konstruksi Metode Transformasi Diferensial Multi-Step (Multi-Step Differential Transform Method) untuk Model SEIRS Autonomous dan Nonautonomous
Abstract
Pemodelan matematika telah banyak digunakan untuk memahami permasalahan nyata. Model matematika dapat diselesaikan secara analitik. Namun, apabila model matematika tersebut semakin kompleks, maka solusi analitik tidak mudah diperoleh dan pendekatan numerik digunakan. Dalam artikel ini, pendekatan numerik dengan Metode Transformasi Diferensial (MTD) multi-step yang menghasilkan solusi deret konvergen digunakan untuk mencari solusi dari model matematika penyebaran penyakit SEIRS yang autonomous dan non-autonomous. Metode ini dikenal juga dengan metode semi analitik karena kita dapat menuliskan solusi analitik dari model yang dicarikan solusinya. Dalam artikel akan dikonstruksi metode tranformasi diferensial untuk model SEIRS autonomous dan nonautonomous dan menganalisis akurasi dengan cara membandingkan dengan metode Runge-Kutta. Metode transformasi diferensial multi-step dapat memberikan aproksimasi solusi yang baik dari model matematika SEIRS autonomous dan non-autonomous. Namun, kinerja dari metode ini lebih baik pada model autonomous.
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DOI: https://doi.org/10.24198/jmi.v16.n1.27630.52-60
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