In this paper, we are going to present a class of nonlinear equation solving methods. Steffensen’s method is a simple method for solving a nonlinear equation. By using Steffensen’s method and by combining this metho...In this paper, we are going to present a class of nonlinear equation solving methods. Steffensen’s method is a simple method for solving a nonlinear equation. By using Steffensen’s method and by combining this method with it, we obtain a new method. It can be said that this method, due to not using the function derivative, would be a good method for solving the nonlinear equation compared to Newton’s method. Finally, we will see that Newton’s method and Steffensen’s hybrid method both have a two-order convergence.展开更多
Synchronization is one of the most important characteristics of dynamic systems.For this paper,the authors obtained results for the nonlinear systems controller for the custom Synchronization of two 4D systems.The fin...Synchronization is one of the most important characteristics of dynamic systems.For this paper,the authors obtained results for the nonlinear systems controller for the custom Synchronization of two 4D systems.The findings have allowed authors to develop two analytical approaches using the second Lyapunov(Lyp)method and the Gardanomethod.Since the Gardano method does not involve the development of special positive Lyp functions,it is very efficient and convenient to achieve excessive systemSYCR phenomena.Error is overcome by using Gardano and overcoming some problems in Lyp.Thus we get a great investigation into the convergence of error dynamics,the authors in this paper are interested in giving numerical simulations of the proposed model to clarify the results and check them,an important aspect that will be studied is Synchronization Complete hybrid SYCR and anti-Synchronization,by making use of the Lyapunov expansion analysis,a proposed control method is developed to determine the actual.The basic idea in the proposed way is to receive the evolution of between two methods.Finally,the present model has been applied and showing in a new attractor,and the obtained results are compared with other approximate results,and the nearly good coincidence was obtained.展开更多
The application of optimization methods to prediction issues is a continually exploring field.In line with this,this paper investigates the connectedness between the infected cases of COVID-19 and US fear index from a...The application of optimization methods to prediction issues is a continually exploring field.In line with this,this paper investigates the connectedness between the infected cases of COVID-19 and US fear index from a forecasting perspective.The complex characteristics of implied volatility risk index such as non-linearity structure,time-varying and nonstationarity motivate us to apply a nonlinear polynomial Hammerstein model with known structure and unknown parameters.We use the Hybrid Particle Swarm Optimization(HPSO)tool to identify the model parameters of nonlinear polynomial Hammerstein model.Findings indicate that,following a nonlinear polynomial behaviour cascaded to an autoregressive with exogenous input(ARX)behaviour,the fear index in US financial market is significantly affected by COVID-19-infected cases in the US,COVID-19-infected cases in the world and COVID-19-infected cases in China,respectively.Statistical performance indicators provided by the developed models show that COVID-19-infected cases in the US are particularly powerful in predicting the Cboe volatility index compared to COVID-19-infected cases in the world and China(MAPE(2.1013%);R2(91.78%)and RMSE(0.6363 percentage points)).The proposed approaches have also shown good convergence characteristics and accurate fits of the data.展开更多
文摘In this paper, we are going to present a class of nonlinear equation solving methods. Steffensen’s method is a simple method for solving a nonlinear equation. By using Steffensen’s method and by combining this method with it, we obtain a new method. It can be said that this method, due to not using the function derivative, would be a good method for solving the nonlinear equation compared to Newton’s method. Finally, we will see that Newton’s method and Steffensen’s hybrid method both have a two-order convergence.
文摘Synchronization is one of the most important characteristics of dynamic systems.For this paper,the authors obtained results for the nonlinear systems controller for the custom Synchronization of two 4D systems.The findings have allowed authors to develop two analytical approaches using the second Lyapunov(Lyp)method and the Gardanomethod.Since the Gardano method does not involve the development of special positive Lyp functions,it is very efficient and convenient to achieve excessive systemSYCR phenomena.Error is overcome by using Gardano and overcoming some problems in Lyp.Thus we get a great investigation into the convergence of error dynamics,the authors in this paper are interested in giving numerical simulations of the proposed model to clarify the results and check them,an important aspect that will be studied is Synchronization Complete hybrid SYCR and anti-Synchronization,by making use of the Lyapunov expansion analysis,a proposed control method is developed to determine the actual.The basic idea in the proposed way is to receive the evolution of between two methods.Finally,the present model has been applied and showing in a new attractor,and the obtained results are compared with other approximate results,and the nearly good coincidence was obtained.
基金This research has been funded by Scientific Research Deanship at University of Ha’il,Saudi Arabia through Project number RG-20210.
文摘The application of optimization methods to prediction issues is a continually exploring field.In line with this,this paper investigates the connectedness between the infected cases of COVID-19 and US fear index from a forecasting perspective.The complex characteristics of implied volatility risk index such as non-linearity structure,time-varying and nonstationarity motivate us to apply a nonlinear polynomial Hammerstein model with known structure and unknown parameters.We use the Hybrid Particle Swarm Optimization(HPSO)tool to identify the model parameters of nonlinear polynomial Hammerstein model.Findings indicate that,following a nonlinear polynomial behaviour cascaded to an autoregressive with exogenous input(ARX)behaviour,the fear index in US financial market is significantly affected by COVID-19-infected cases in the US,COVID-19-infected cases in the world and COVID-19-infected cases in China,respectively.Statistical performance indicators provided by the developed models show that COVID-19-infected cases in the US are particularly powerful in predicting the Cboe volatility index compared to COVID-19-infected cases in the world and China(MAPE(2.1013%);R2(91.78%)and RMSE(0.6363 percentage points)).The proposed approaches have also shown good convergence characteristics and accurate fits of the data.
