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Applied Mathematics 2014年第8期5卷 1252-1266页

作者： Mathew Remilekun Odekunle Michael Otokpa Egwurube Adetola Olaide Adesanya Mfon Okon Udo Department of Mathematics and Statistics Cross River University of Technology Calabar Nigeria Department of Mathematics Modibbo Adama University of Technology Yola Nigeria

Theory has it that increasing the step length improves the accuracy of a method. In order to affirm this we increased the step length of the concept in [1] by one to get k = 5. The technique of collocation and interpolation of the power series approximate solution at some selected grid points is considered so as to generate continuous linear multistep methods with constant step sizes. Two, three and four interpolation points are considered to generate the continuous predictor-corrector methods which are implemented in block method respectively. The proposed methods when tested on some numerical examples performed more efficiently than those of [1]. Interestingly the concept of self starting [2] and that of constant order are reaffirmed in our new methods.

关键词： Step Length Power Series Block Predictor Block corrector Constant Order Step Size Grid Points Self Starting Efficiency

A parallel method for numerical solution of delay differential equations

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Journal of Harbin Institute of Technology(New Series) 2000年第3期7卷 37-39页

作者：丁效华刘明珠 Dept. of Mathematics Harbin Institute of Technology Harbin 150001 China

A parallel diagonally iterated Runge Kutta (PDIRK) method is constructed to solve stiff initial value problems for delay differential equations. The order and stability of this PDIRK method has been analyzed, and the iteration parameters of the method are tuned in such a way that fast convergence to the value of corrector is achieved.

关键词： diagonally implicit RK methods parallel method corrector

HOMOGENIZATION OF SOME LINEAR AND SEMILINEAR SCHRDINGER EQUATIONS WITHREAL POTENTIAL

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Acta Mathematica Scientia 2001年第1期21卷 137-144页

作者：姚正安 Department of Mathematics Zhongshan University Guangzhou 510275 China

This paper considers the initial and boundary value problem of some linear and semilinear Schrodinger equation with real potential and H01 initial data. The author obtains the homogenization of linear and semilinear S... 详细信息

关键词： corrector homogenization semilinear Schrodinger equation

Four Steps Continuous Method for the Solution of y″= f(x, y, y′)

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American Journal of Computational Mathematics 2013年第2期3卷 169-174页

作者： Adetola Olaide Adesanya Mattew Remilekun Odekunle Mfon Odo Udoh Department of Mathematics and Statistics Cross River State University of Technology Calabar Nigeria Department of Mathematics Modibbo Adama University of Technology Yola Nigeria

This paper proposes a continuous block method for the solution of second order ordinary differential equation. Collocation and interpolation of the power series approximate solution are adopted to derive a continuous implicit linear multistep method. Continuous block method is used to derive the independent solution which is evaluated at selected grid points to generate the discrete block method. The order, consistency, zero stability and stability region are investigated. The new method was found to compare favourably with the existing methods in term of accuracy.

关键词： Predictor corrector Collocation Interpolation Power Series Approximant Continuous Block Method

Optical System Design of Telescope Based on Mixed Modulation Diffractive Lens

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Journal of Applied Mathematics and Physics 2018年第11期6卷 2322-2329页

作者： Fei Li Xueying Jin Mengyu Wang Keyi Wang Department of Precision Machinery and Precision Instrumentation University of Science and Technology of China Hefei China

Using of diffractive optical elements (DOE) in the Schupmann system offer a new way for the construction of ultra-large aperture telescope. The Fresnel corrector, one of the DOEs, is the key device in the Schupmann system, which is used to correct the chromatic aberration introduced by the diffractive primary lens called Magnifying Glass. Generally, in a large aperture telescope (>20 m), the Fresnel corrector is a diffractive lens with a large aperture and a small f-number, which is difficult to process. In this article, an improved device with a small F number but a large rim feature size, called amplitude and phase hybrid modulation Fresnel diffractive optical element (APHMFDOE), is used here as the Fresnel corrector. First, APHMFDOE with appropriate parameters is designed to match the dispersion of the Magnifying Glass so that the system meets the achromatic condition. Second, the optical characteristics of this improved system are simulated and compared with those of the general system based on the conventional Fresnel corrector. Our approach introduces a new dispersion correction device, which not only can eliminate the chromatic aberration caused by Magnifying Glass, but also can reduce the processing difficulty of Fresnel corrector.

关键词： Fresnel corrector Diffractive Telescope Imaging System

A PCGM algorithm for solving linear equations

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Journal of Chongqing University 2013年第2期12卷 85-90页

作者：夏林林 ZHANG Li 吴开腾 College of Mathematics and Soft Science Sichuan Normal University Key Laboratory of Numerical Simulation in the Sichuan Provincial College Neijiang Normal University

Based on the predictor corrector, we developed a new improved gradient method named the predictor corrector gradient algorithm (PCGM), which is useful for solving linear equations with symmetric positive definite of coefficient *** improve the speed of convergence of traditional gradient method, we let values of original iterative formula be viewed as forecast ***, they are corrected by a new iterative formula through introducing corresponding step ***, a feasible and efficient algorithm is *** experiments indicate that PCGM method not only improve the accuracy and the speed of convergence, but also greatly reduce the number of steps to *** simple algorithm is easy to be realized and operated.

关键词： predictor corrector gradient method symmetric positive definite convergence speed

分数阶Jerk系统的动力学分析及在保密通信方面的应用

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咸阳师范学院学报 2011年第6期26卷 15-19页

作者：翟海峰张晓刚漆翻慧兰州交通大学数理与软件工程学院甘肃兰州730070

通过Adams-Bashforth-Moulton方法和predictor corrector algorithm方法并结合分数阶稳定性理论,辅助以相图、脉冲响应曲线、分叉图等分析了Jerk系统的动力学行为;引入反馈控制法对系统进行控制,最终得到理想的结果,并将其应用于保密通... 详细信息

通过Adams-Bashforth-Moulton方法和predictor corrector algorithm方法并结合分数阶稳定性理论,辅助以相图、脉冲响应曲线、分叉图等分析了Jerk系统的动力学行为;引入反馈控制法对系统进行控制,最终得到理想的结果,并将其应用于保密通讯。Matlab数值仿真验证了其有效性。

关键词：分数阶混沌系统 Adams—Bashforth—Moulton方法 predictor corrector algorithm法反馈控制保密通信