An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations

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Soleymani F., Shateyi S., ÖZKUM G.

SCIENTIFIC WORLD JOURNAL, 2013 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası:
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1155/2013/837243
  • Dergi Adı: SCIENTIFIC WORLD JOURNAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Kocaeli Üniversitesi Adresli: Evet

Özet

We develop a high-order fixed point type method to approximate a multiple root. By using three functional evaluations per full cycle, a new class of fourth-order methods for this purpose is suggested and established. The methods from the class require the knowledge of the multiplicity. We also present a method in the absence of multiplicity for nonlinear equations. In order to attest the efficiency of the obtained methods, we employ numerical comparisons alongside obtaining basins of attraction to compare them in the complex plane according to their convergence speed and chaotic behavior.