OPTIMIZATION BY THE CONVERGENCE CONTROL PARAMETER IN ITERATIVE METHODS
JOURNAL OF APPLIED MATHEMATICS AND COMPUTATIONAL MECHANICS, cilt.23, sa.2, ss.105-116, 2024 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 23 Sayı: 2
- Basım Tarihi: 2024
- Doi Numarası: 10.17512/jamcm.2024.2.09
- Dergi Adı: JOURNAL OF APPLIED MATHEMATICS AND COMPUTATIONAL MECHANICS
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Sayfa Sayıları: ss.105-116
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Hacettepe Üniversitesi Adresli: Evet
Özet
The classical iterative methods, such as the fixed point iteration, the Adomian decomposition method and the homotopy analysis method are discussed in the present paper. It is proven that adding a convergence control parameter into these makes them powerful and rapidly converging to the true solution, whilst the classical correspondences may fail to or slowly converge to the desired solution. The key is to demonstrate the presence of a continuous interval of the convergence control parameter for the considered problem. This allows convergence of such modified iterative methods with an optimum convergence control parameter obtained from squared residual errors of either the original equation or the derivative of iterative solution with respect to the convergence control parameter.