جستجوی مقالات مرتبط با کلیدواژه "nonlinear equations" در نشریات گروه "علوم پایه"

In this paper,a new family of eighth-order iterative methods for solving simple roots of nonlinear equations is developed.Each member of the proposed family requires four functional evaluations in each iteration that it is optimal according to the sense of Kung-Traub’s conjecture.They have four self-accelerating parameters that are calculated using the adaptive method.The R-order of convergence has increased from 8 to 16 (maximum improvement).

Improvement and change in teachers' knowledge and practice are likely to bring about changes in teacher growth, varieties in teachers' instructional techniques and strategies as well as enhancement in student learning. In the field of language learning and teaching, many linguistic and non-linguistic issues have been examined to explain the role of psychological issues and individual differences in foreign language learning, However, the role of positive emotions has not been investigated sufficiently among EFL teachers. Therefore, the present study has investigated gender and teaching experience on the well-being, professional growth and self-concept of Iranian English teachers. The present research in terms of practical purpose and in terms of the method of collecting information, is a survey type, and in terms of execution time, it is cross-sectional, and in terms of execution logic, it is deductive-inductive. The current research community consists of 220 Iranian English language teachers in private language learning institutions in Tabriz who have at least 5 years of teaching experience. In the current research, the main measurement tool is a questionnaire, which is one of the common research tools and a direct method for obtaining research data. According to the nature of the subject, the research method is a quantitative method. The gathered data was analyzed using correlation analysis and structural equation modelling (SEM). The software packages SPSS 24.0 and Amos 8 were used for descriptive statistics and correlation analyses, respectively. The results revealed that there is a significant structural relationship between well-being and self-concept with the mediation of gender and experience. However, there is no significant structural relationship between well-being and professional development with the mediation of gender and experience.

This research was done to design a competitive advantage model with an emphasis on brand identity in the clothing industry. The statistical population in the qualitative phase includes 15 experts and managers of clothing manufacturing companies who were selected in a non-random way. The main tool of data collection is a semi-structured in-depth interview. Qualitative data analysis was done with the method of database theory and using MAXQDA software. The statistical population in the quantitative part, statistical population in the quantitative part included all customers of clothing products in Tehran city, based on which a sample of 384 people was selected using Morgan's table. Data collection was done in the quantitative section using a questionnaire and data analysis with the partial least squares method and SMART-PLS software. Based on the obtained paradigm model, the components related to competitive advantage with emphasis on brand identity in the Clothing industry in six categories of causal factors (brand identity and competitiveness factors), background conditions (product and service advantage), central phenomenon (competitive advantage), strategies (company planning), intervening conditions (competition management factors) and outcomes (brand loyalty, brand identity, brand orientation and market share) were identified.

The purpose of this research is to identify effective factors in the evaluation of organizational performance in Iran Telecommunication Company using the fuzzy hierarchical analysis method of Mikhailov along with interpretive structural modelling. First, by studying the literature and research history, more than 14 general factors affecting the evaluation of organizational performance were identified, which were identified using a questionnaire and based on the opinions of 22 experts, among them 9 factors with a total of about 90\% of the opinions that have the most importance in influencing were determined to be considered for levelling. The levelling of these factors in terms of importance was based on the FAHP method and the ISM method. Due to the use of Mikhailov's fuzzy hierarchical analysis method along with interpretive structural modelling to identify and stratify the influencing factors on the evaluation of organizational performance, this research is considered an innovative model for studying the evaluation of organizational performance. According to the findings of the review of the above factors, which was based on ISM, the ``public environment" factor has gained the most importance, and this factor, along with the ``strategy" factors, as well as ``processes and methods" and ``interactive environment" as basic factors in The final research model was determined.

The adaptive technique enables us to achieve the highest efficiency index theoretically and practically. The idea of introducing an adaptive self-accelerator (via all the old information for Steffensen-type methods) is new and efficient to obtain the highest efficiency index. In this work, we have used four self-accelerating parameters and have increased the order of convergence from 8 to 16, i. e. any new function evaluations improve the convergence order up to 100%. The numerical results are compared without and with memory methods. It confirms that the proposed methods have more efficiency index.

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.

In this study, we propose a family of iterative procedures with no deriva-tives for calculating multiple roots of one-variable nonlinear equations. We also present an iterative technique to approximate the multiplicity of the roots. The new class is optimal since it fits the Kung–Traub hypothesis and has second-order convergence. Derivative-free methods for calculating mul-tiple roots are rarely found in literature, especially in the case of one-step methods, which are the simplest ones in terms of their structure. Moreover, this new family contains almost all the existing single-step derivative-free iterative schemes as its special cases, with an additional degree of freedom. Several results are used to confirm its theoretical order of convergence. Through the complex discrete dynamics analysis, the stability of the sug-gested class is illustrated, and the most stable methods are found. Several test problems are included to check the performance of the proposed meth-ods, whether the multiplicity of the roots is estimated or known, comparing the numerical results with those obtained by other methods.

In this work, the dynamics of the Modified Halley's method to multiple roots are established. We find the fixed and critical points. The stable and unstable behaviors are studied. The parameter space associated with the method is studied and finally, some dynamical planes that show different aspects of the dynamics of this method are presented.

In this paper, by utilizing the Sine-Gordan expansion method, soliton solutions of the higher-order improved Boussinesq equation, Kuramoto-Sivashinsky equation, and seventh-order Sawada-Kotera equation are obtained. Given partial differential equations are reduced to ordinary differential equations, by choosing the compatible wave transformation associated with the structure of the equation. Based on the solution of the Sine-Gordan equation, a polynomial system of equations is obtained according to the principle of homogeneous balancing. The solution of the outgoing system gives the parameters which are included by the solution. Plot3d and Plot2d graphics are given in detail. As a result, many different graphic models are obtained from soliton solutions of equations that play a very important role in mathematical physics and engineering.

One of the major problems in applied mathematics and engineering sciences is solving nonlinear equations. In this paper, a family of eight-order interval methods for computing rigorous bounds on the simple zeros of nonlinear equations is presented. We present the convergence and er-ror analysis of the introduced methods. Also, the introduced methods are compared with the well-known interval Newton method and interval Ostrowski-type methods. Finally, we propose a technique based on the combination of the newly introduced approach with the extended interval arithmetic to find all of the roots of a nonlinear equation that are located in an initial interval.

In the present paper, at first, we propose a new two-step iterative method for solving nonlinear equations. This scheme is based on the Steffensen's method, in which the order of convergence is four. This iterative method requires only three functions evaluation in each iteration, therefore it is optimal in the sense of the Kung and Traub conjecture. Then we extend it to the method with memory, which the order of convergence is six. Finally, numerical examples indicate that theobtained methods in terms of accuracy and computational cost are superior to thefamous forth-order methods.

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.

It is well known that, one of the useful and rapid methods for a nonlinear system of algebraic equations is Newton's method. Newton's method has at least quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood of the solution. In this paper, a differential continuation method is presented for solving the nonlinear system of algebraic equations whose Jacobian matrix is singular at the solution. For this purpose, at first, an auxiliary equation named the homotopy equation is constructed. Then, by differentiating from the homotopy equation, a system of differential equations is replaced instead of the target problem and solved. In other words, the solution of the nonlinear system of algebraic equations with singular Jacobian is transformed to the solution of a system of differential equations. Some numerical tests are presented at the end and the computational efficiency of the method is described.

In this study, we present two two-step methods to solve parameterized generalized inverse eigenvalue problems that appear in diverse areas of computation and engineering applications.  At the first step,  we  transfer the inverse eigenvalue problem into a  system of nonlinear equations by using of the Golub-Kahan bidiagonalization. At the second step, we use Newton's and Quasi-Newton's  methods for the numerical solution of system of nonlinear equations. Finally, we present some numerical examples which show that our methods are applicable for solving the parameterized inverse eigenvalue problems.

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.

In this paper, a completely new statistical-based approach is developed for solving the system of nonlinear equations. The developed approach utilizes the characteristics of the normal distribution to search the solution space. The normal distribution is generally introduced by two parameters, i.e., mean and standard deviation. In the developed algorithm, large values of standard deviation enable the algorithm to escape from a local optimum, and small values of standard deviation help the algorithm to find the global optimum. In the following, six benchmark tests and thirteen benchmark case problems are investigated to evaluate the performance of the Normal Distribution-based Algorithm (NDA). The obtained statistical results of NDA are compared with those of PSO, ICA, CS, and ACO. Based on the obtained results, NDA is the least time-consuming algorithm that gets high-quality solutions. Furthermore, few input parameters and simple structure introduce NDA as a user friendly and easy-to-understand algorithm.

In this article, a new powerful analytical method, the Tamimi-Ansari method (TAM), has been introduced to solve some nonlinear problems that have been used in physics. This method does not require any hypothesis to counter with the nonlinear term. These results are compared with the exact solution and two other analytical methods. A few examples have been presented to show that this method is effective and reliable.

In this work, we have created the four families of memory methods by convergence rates of three, six, twelve, and twenty-four. Every member of the proposed class has a self-accelerator parameter. And, it has approximated by using Newton’s interpolating polynomials. The new iterative with memory methods have a 50% improvement in the order of convergence.

In this paper, we present a nonlinear parametric method to stabilize descriptor fractional discrete time linear system practically. Parametric methods with the free parameters can be adjusted to obtain better performance responses like minimum norm in state feedback. The aim is assigning desirable eigenvalues to obtain satisfactory responses by forward state feedback and forward and propositional state feedback in new systems with large matrices. However, finding the solution to nonlinear parametric equations makes some errors. In partial eigenvalue assignment, just a part of the open-loop spectrum of the standard linear systems is reassigned, while leaving the rest of the spectrum invariant. The size of matrices, state, and input vectors are decreased and the stability is kept. At the end, summary and conclusions are proposed and the convergence of state vectors in the descriptor fractional discrete-time system to zero is also shown by figures in a numerical example. Our method is also compared with another method with one of orthogonality relations in our article and example.

A fourth-order and rapid numerical algorithm, utilizing a procedure as Runge–Kutta methods, is derived for solving nonlinear equations. The method proposed in this article has the advantage that it, requiring no calculation of higher derivatives, is faster than the other methods with the same order of convergence. The numerical results obtained using the developed approach are compared to those obtained using some existing iterative methods, and they demonstrate the efficiency of the present approach.