Approximate solutions of nonlinear boundary value problems by collocation methods compared to newer methods

---

Durak B., Özer H. Ö., Sezgin A., Sakman L. E.

SAKARYA UNIVERSITY JOURNAL OF SCIENCE, cilt.27, sa.6, ss.1345-1354, 2023 (Scopus, TRDizin)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 27 Sayı: 6
• Basım Tarihi: 2023
• Doi Numarası: 10.16984/saufenbilder.1342645
• Dergi Adı: SAKARYA UNIVERSITY JOURNAL OF SCIENCE
• Derginin Tarandığı İndeksler: Scopus, Academic Search Premier, Business Source Elite, Business Source Premier, TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.1345-1354
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• İstanbul Üniversitesi-Cerrahpaşa Adresli: Evet

Özet

A large variety of new methods are being developed for fast and efficient solutions of nonlinear boundary value problems.  Some of these methods are, Adomian decomposition (ADM), differential transform (DTM), least squares vector machines (LSSVMM), and multiple variational iteration (MVIM).  A natural question arises as to how efficient and simple to use these newer methods are compared to classical methods.  One of the simplest and widely applicable classical methods is the collocation method.  The overall performance of collocation method and the newer methods are compared on a number of problems, which were previously used to benchmark the newer methods.  It is concluded that, at least for the problems considered, the collocation method performs as successfully as the newer methods.