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.
Torkashvand,V , Kazemi,M and Moccari,M . (2021). Structure a Family of Three-Step with-Memory Methods for Solving Nonlinear Equations and Their Dynamics. Mathematical Analysis and Convex Optimization, 2(2), 119-137. doi: 10.22034/maco.2.2.12
MLA
Torkashvand,V , , Kazemi,M , and Moccari,M . "Structure a Family of Three-Step with-Memory Methods for Solving Nonlinear Equations and Their Dynamics", Mathematical Analysis and Convex Optimization, 2, 2, 2021, 119-137. doi: 10.22034/maco.2.2.12
HARVARD
Torkashvand V, Kazemi M, Moccari M. (2021). 'Structure a Family of Three-Step with-Memory Methods for Solving Nonlinear Equations and Their Dynamics', Mathematical Analysis and Convex Optimization, 2(2), pp. 119-137. doi: 10.22034/maco.2.2.12
CHICAGO
V Torkashvand, M Kazemi and M Moccari, "Structure a Family of Three-Step with-Memory Methods for Solving Nonlinear Equations and Their Dynamics," Mathematical Analysis and Convex Optimization, 2 2 (2021): 119-137, doi: 10.22034/maco.2.2.12
VANCOUVER
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. doi: 10.22034/maco.2.2.12
Mathematical Analysis and Convex Optimization
