Mathematical Analysis and Convex Optimization
آنالیز ریاضی و بهینه سازی محدب
MACO
Basic Sciences
http://maco.lu.ac.ir
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2021
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Structure a Family of Three-Step with-Memory Methods for Solving Nonlinear Equations and Their Dynamics
Applied Mathematics
Applied Mathematics
پژوهشي
Research Article
In this work, we will ﬁrst propose an optimal three-step without-memory<br>
method for solving nonlinear equations. Then, by introducing the self-accelerating<br>
parameters, the with-memory-methods have been built. They have a ﬁfty-nine<br>
percentage improvement in the convergence order. The proposed methods have<br>
not the problems of calculating the function derivative. We use these Steffensen-<br>
type methods to solve nonlinear equations with simple zeroes with the appropri-<br>
ate initial approximation of the root. we have solved a few nonlinear problems<br>
to justify the theoretical study. Finally, are described the dynamics of the with-<br>
memory method for complex polynomials of degree two.
With-memory method, Basin of attraction, Accelerator parameter,R- order convergence,Nonlinear equations
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http://maco.lu.ac.ir/browse.php?a_code=A-10-113-1&slc_lang=en&sid=1
Vali
Torkashvand
torkashvand1978@gmail.com
`1003194753284600941`

1003194753284600941
Yes
Member of Young Researchers and Elite club Shahr-e-Qods Branch Islamic Azad University, Tehran, Iran
Manochehr
Kazemi
univer_ka@yahoo.com
`1003194753284600942`

1003194753284600942
No
Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran
Mandana
Moccari
m_moccari@yahoo.com
`1003194753284600943`

1003194753284600943
No
Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran