Komputasi Numerik Metode Iteratif Half-Sweep Preconditioned Gauss-Seidel Untuk Memecahkan Persamaan Resepan Pecahan Waktu
Abstract
Dalam penelitian ini, peneliti berusaha memperoleh persamaan aproksimasi beda hingga dari diskritisasi persamaan resapan pecahan waktu linier satu dimensi dengan menggunakan turunan pecahan waktu Caputo. Suatu sistem persamaan linier akan dibuat dengan menggunakan persamaan aproksimasi beda hingga Caputo. Kemudian hasil dari system persamaan linier tersebut diselesaikan dengan menggunakan metode iterasif numerik Half-Sweep Preconditioned Gauss-Seidel (HSPGS) dimana efektivitasnya akan dibandingkan dengan metode Preconditioned Gauss-Seidel (PGS), (dikenal juga sebagai Full-Sweep Preconditioned Gauss- Seidel (FSPGS)) dan Gauss-Seidel (GS) sebagai metode kontrol. Contoh masalah juga disajikan untuk menguji efektivitas metode yang diusulkan. Temuan penelitian ini menunjukkan bahwa metode iteratif yang diusulkan yaitu HSPGS lebih unggul dibandingkan dengan metode FSPGS dan GS.
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