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(10 citation statements)

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“…It is obvious that the iterative method (10) requires the operation of the second derivative of the function f (x). In order to avoid computing the second derivative, we introduce an approximant of the second derivative by using Taylor's series.…”

confidence: 99%

“…It is obvious that the iterative method (10) requires the operation of the second derivative of the function f (x). In order to avoid computing the second derivative, we introduce an approximant of the second derivative by using Taylor's series.…”

confidence: 99%

“…In [9], Abbasbandy et al present an efficient numerical algorithm for solving nonlinear algebraic equations based on Newton-Raphson method and homotopy analysis method. Noor and Khan suggest and analyze a new class of iterative methods by using the homotopy perturbation method in [10]. In 2015, Wang et al [11] deduce a general family of n-point Newton type iterative methods for solving nonlinear equations by using direct Hermite interpolation.…”

confidence: 99%

“…In the past years, many modified iterative methods have been developed for finding the simple roots of a nonlinear equation f (t) = 0, which is a common and important problem in science and engineering [1,9,12,15]. Several classical methods, such as Newton, Halley or Ostrowskis methods, are utilized to improve the local order of convergence [2,[5][6][7][8]11].…”

confidence: 99%

“…Finally, let us point out that HPM has been improving, developing and modifying, until to the present time. Consequently, today exist various solver techniques that are based, to a greater or lesser extent, on the basic HPM assumptions (Noor & Khan, 2012;Zhang et al, 2015;Tripathi & Mishra, 2016;Bota & Caruntu, 2017). Here is given a brief theoretical background about the HPM and some sufficient conditions to its convergence.…”

confidence: 99%