جستجوی مقالات مرتبط با کلیدواژه « Basin of attraction » در نشریات گروه « علوم پایه »
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In this work, we have proposed a general manner to extend some two-parametric with-memory methods to obtain simple roots of nonlinear equations. Novel improved methods are two-step without memory and have two self-accelerator parameters that do not have additional evaluation. The methods have been compared with the nearest competitions in various numerical examples. Anyway, the theoretical order of convergence is verified. The basins of attraction of the suggested methods are presented and corresponded to explain their interpretation.Keywords: With-Memory Method, Basin Of Attraction, Accelerator Parameter, $R$-Order Convergence, Nonlinear Equations}
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In this paper, the degree of convergence of Newton’s method has been increased from two to four using two function evaluations. For this purpose,the weakness of Newton’s method, derivative calculation has been eliminated with a proper approximation of the previous data. Then, by entering two selfaccelerating parameters, the family new with-memory methods with Steffensen-Like memory with convergence orders of 2.41, 2.61, 2.73, 3.56, 3.90, 3.97, and 4 are made. This goal has been achieved by approximating the self-accelerator parameters by using the secant method and Newton interpolation polynomials.Finally, we have examined the dynamic behavior of the proposed methods for solving polynomial equations.Keywords: With-memory method, Accelerator parameter, Basin of attraction, Efficiency index, Newton’s interpolatory polynomial}
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The current research develops a derivative-free family without memory methods. The proposed method consisting of two steps and one parameter for solving nonlinear equations is brought forward.\,The basin of attraction of the proposed methods has investigated using different weight functions.\,Numerical examples are experimented with to check the performance of the proposed schemes. Furthermore, the theoretical order of convergence is confirmed on the experiment work.Keywords: Iterative method, Convergence order, Basin of attraction, Nonlinear equation}
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In this work, we have constructed the with memory two-step method with four convergence degrees by entering the maximum self-accelerator parameter(three parameters). Then, using Newton’s interpolation, a with-memory method with a convergence order of 7.53 is constructed. Using the information of all the steps, we will improve the convergence order by one hundred percent, and we will introduce our method with convergence order 8. Numerical examples demonstrate the exceptional convergence speed of the proposed method and confirm theoretical results. Finally, we have presented the dynamics of the adaptive method and other without-memory methods for complex polynomials of degrees two, three, and four. The basins of attraction of existing with-memory methods are present and compared to illustrate their performance.Keywords: Nonlinear equations, Basin of attraction, Adaptive methods, R-order convergence, Self accelerating parameter}
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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.
Keywords: With-memory method, Basin of attraction, Accelerator parameter, R- order convergence, Nonlinear equations} -
This paper deals with the study of relaxed conditions for semi-local convergence for a general iterative method, k-step Newton's method, using majorizing sequences. Dynamical behavior of the mentioned method is also analyzed via Julia set and basins of attraction. Numerical examples of nonlinear systems of equations will be examined to clarify the given theory.
Keywords: Majorizing sequence, High order of convergence, Semi-local convergence, Julia set, Basin of attraction}
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