An iterative solver in the presence and absence of multiplicity for nonlinear equations.
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.
Young Researchers and Elite Club, Zahedan Branch, Islamic Azad University, Zahedan, Iran.
Fazlollah
F
Soleymani
Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa.
Stanford
S
Shateyi
Department of Mathematics, Science and Letter Faculty, Kocaeli University, Umuttepe Campus, Kocaeli, Turkey.
Gülcan
G
Özkum
D008962:Models, Theoretical