As an important aspect of applications, it is discussed how to find periodic solutions for ordinary differential equations. By using the homotopy method, a global method for finding those solutions is proposed.
In this paper, we derive two higher order multipoint methods for solving nonlinear equations. The methodology is based on Ostrowski’s method and further developed by using cubic interpolation process. The adaptation ...In this paper, we derive two higher order multipoint methods for solving nonlinear equations. The methodology is based on Ostrowski’s method and further developed by using cubic interpolation process. The adaptation of this strategy increases the order of Ostrowski’s method from four to eight and its efficiency index from 1.587 to 1.682. The methods are compared with closest competitors in a series of numerical examples. Moreover, theoretical order of convergence is verified on the examples.展开更多
In a recent paper, Noor and Khan [M. Aslam Noor, & W. A. Khan, (2012) New Iterative Methods for Solving Nonlinear Equation by Using Homotopy Perturbation Method, Applied Mathematics and Computation, 219, 3565-3574...In a recent paper, Noor and Khan [M. Aslam Noor, & W. A. Khan, (2012) New Iterative Methods for Solving Nonlinear Equation by Using Homotopy Perturbation Method, Applied Mathematics and Computation, 219, 3565-3574], suggested a fourth-order method for solving nonlinear equations. Per iteration in this method requires two evaluations of the function and two of its first derivatives;therefore, the efficiency index is 1.41421 as Newton’s method. In this paper, we modified this method and obtained a family of iterative methods for appropriate and suitable choice of the parameter. It should be noted that per iteration for the new methods requires two evaluations of the function and one evaluation of its first derivatives, so its efficiency index equals to 1.5874. Analysis of convergence shows that the methods are fourth-order. Several numerical examples are given to illustrate the performance of the presented methods.展开更多
This paper deals with the problems of finding periodic solutions for the third order ordinary differential equations of the form (1) where T is a fixed positive number and f satisfies some additional conditions which ...This paper deals with the problems of finding periodic solutions for the third order ordinary differential equations of the form (1) where T is a fixed positive number and f satisfies some additional conditions which will be stated later.The periodicity problem has been one of main topics in the qualitative theory of ordinary展开更多
空间谱测向算法是一种估计信源波达方向(Direction of Arrival, DOA)的高分辨测向算法,具有布阵灵活、分辨率高的特点,已在实际工程中得到广泛应用。受组阵后单元天线幅相误差大、阵列所处传播环境复杂的影响,造成测向接收机采集到的各...空间谱测向算法是一种估计信源波达方向(Direction of Arrival, DOA)的高分辨测向算法,具有布阵灵活、分辨率高的特点,已在实际工程中得到广泛应用。受组阵后单元天线幅相误差大、阵列所处传播环境复杂的影响,造成测向接收机采集到的各路数据失真严重,理论阵列流型失效,从而严重影响测向算法的性能。为提高空间谱算法在实测天线幅相响应与理论值差异大时的测向稳定性,提出了一种基于天线幅相响应修正的测向算法,通过将信号实际幅相响应引入算法并做加权处理,降低了空间谱测向的误差,该方法具有良好的实际工程应用价值。展开更多
文摘As an important aspect of applications, it is discussed how to find periodic solutions for ordinary differential equations. By using the homotopy method, a global method for finding those solutions is proposed.
基金Foundation item： Supported by the National Science Foundation of China（10701066） Supported by the National Foundation of the Education Department of Henan Province（2008A110022）
文摘In this paper, we derive two higher order multipoint methods for solving nonlinear equations. The methodology is based on Ostrowski’s method and further developed by using cubic interpolation process. The adaptation of this strategy increases the order of Ostrowski’s method from four to eight and its efficiency index from 1.587 to 1.682. The methods are compared with closest competitors in a series of numerical examples. Moreover, theoretical order of convergence is verified on the examples.
文摘In a recent paper, Noor and Khan [M. Aslam Noor, & W. A. Khan, (2012) New Iterative Methods for Solving Nonlinear Equation by Using Homotopy Perturbation Method, Applied Mathematics and Computation, 219, 3565-3574], suggested a fourth-order method for solving nonlinear equations. Per iteration in this method requires two evaluations of the function and two of its first derivatives;therefore, the efficiency index is 1.41421 as Newton’s method. In this paper, we modified this method and obtained a family of iterative methods for appropriate and suitable choice of the parameter. It should be noted that per iteration for the new methods requires two evaluations of the function and one evaluation of its first derivatives, so its efficiency index equals to 1.5874. Analysis of convergence shows that the methods are fourth-order. Several numerical examples are given to illustrate the performance of the presented methods.
文摘This paper deals with the problems of finding periodic solutions for the third order ordinary differential equations of the form (1) where T is a fixed positive number and f satisfies some additional conditions which will be stated later.The periodicity problem has been one of main topics in the qualitative theory of ordinary
文摘空间谱测向算法是一种估计信源波达方向(Direction of Arrival, DOA)的高分辨测向算法,具有布阵灵活、分辨率高的特点,已在实际工程中得到广泛应用。受组阵后单元天线幅相误差大、阵列所处传播环境复杂的影响,造成测向接收机采集到的各路数据失真严重,理论阵列流型失效,从而严重影响测向算法的性能。为提高空间谱算法在实测天线幅相响应与理论值差异大时的测向稳定性,提出了一种基于天线幅相响应修正的测向算法,通过将信号实际幅相响应引入算法并做加权处理,降低了空间谱测向的误差,该方法具有良好的实际工程应用价值。
