Volume 2, Issue 2 (12-2021)
MACO 2021, 2(2): 119-137 |
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Torkashvand V, Kazemi M, Moccari M. Structure a Family of Three-Step with-Memory Methods for Solving Nonlinear Equations and Their Dynamics. MACO 2021; 2 (2) :119-137
URL: http://maco.lu.ac.ir/article-1-88-en.html
URL: http://maco.lu.ac.ir/article-1-88-en.html
Abstract: (1510 Views)
In this work, we will first propose an optimal three-step without-memory
method for solving nonlinear equations. Then, by introducing the self-accelerating
parameters, the with-memory-methods have been built. They have a fifty-nine
percentage improvement in the convergence order. The proposed methods have
not the problems of calculating the function derivative. We use these Steffensen-
type methods to solve nonlinear equations with simple zeroes with the appropri-
ate initial approximation of the root. we have solved a few nonlinear problems
to justify the theoretical study. Finally, are described the dynamics of the with-
memory method for complex polynomials of degree two.
method for solving nonlinear equations. Then, by introducing the self-accelerating
parameters, the with-memory-methods have been built. They have a fifty-nine
percentage improvement in the convergence order. The proposed methods have
not the problems of calculating the function derivative. We use these Steffensen-
type methods to solve nonlinear equations with simple zeroes with the appropri-
ate initial approximation of the root. we have solved a few nonlinear problems
to justify the theoretical study. Finally, are described the dynamics of the with-
memory method for complex polynomials of degree two.
Keywords: With-memory method, Basin of attraction, Accelerator parameter, R- order convergence, Nonlinear equations
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