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A class of iterative methods with third-order convergence to solve nonlinear equations

✍ Scribed by M. Çetin Koçak

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
223 KB
Volume
218
Category
Article
ISSN
0377-0427

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✦ Synopsis

Algebraic and differential equations generally co-build mathematical models. Either lack or intractability of their analytical solution often forces workers to resort to an iterative method and face the likely challenges of slow convergence, non-convergence or even divergence. This manuscript presents a novel class of third-order iterative techniques in the form of

to solve a nonlinear equation f with the aid of a weight function u. The class currently contains an invert-and-average (g Kia ), an average-and-invert (g Kai ), and an invert-and-exponentiate (g Ke ) branch. Each branch has several members some of which embed second-order Newton's (g N ), third-order Chebychev's (g C ) or Halley's (g H ) solvers. Class members surpassed stand-alone applications of these three well-known methods. Other methods are also permitted as auxiliaries provided they are at least of second order. Asymptotic convergence constants are calculated. Assignment of class parameters to non-members carries them to a common basis for comparison. This research also generated a one-step "solver" that is usable for post-priori analysis, trouble shooting, and comparison.

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