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Establishment of control equations and adjoint equations using block-pulse functions for optimal control of linear systems with time delays
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作者 WANG Xingtao(王兴涛) 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2002年第3期267-269,共3页
Control equation and adjoint equation are established by using block pulse functions, which transforms the linear time varying systems with time delays into a system of algebraic equations and the optimal control prob... Control equation and adjoint equation are established by using block pulse functions, which transforms the linear time varying systems with time delays into a system of algebraic equations and the optimal control problems are transformed into an optimization problem of multivariate functions thereby achieving the optimal control of linear systems with time delays. 展开更多
关键词 block-pulse functions control EQUATIONS ADJOINT EQUATIONS
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利用Block-Pulse函数求解分数阶泊松方程数值解
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作者 赵绚 朱帅 +1 位作者 朱世昕 杨泽民 《数学的实践与认识》 2023年第4期231-237,共7页
借助于二维Block-Pulse函数求解分数阶泊松方程的数值解,并讨论了Dirichlet边界条件,方法是基于Block-Pulse函数的定义及性质,并结合相应的分数阶微分算子矩阵将原问题转化为含有未知变量的代数方程组,进而离散未知变量,求得原问题的数... 借助于二维Block-Pulse函数求解分数阶泊松方程的数值解,并讨论了Dirichlet边界条件,方法是基于Block-Pulse函数的定义及性质,并结合相应的分数阶微分算子矩阵将原问题转化为含有未知变量的代数方程组,进而离散未知变量,求得原问题的数值解.而且还对所提方法进行了误差分析,最后给出的数值算例也验证了所提算法的有效性及可行性. 展开更多
关键词 二维block-pulse函数 泊松方程 数值解 算子矩阵 分数阶
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第六类正交Chebyshev多项式混合Block-Pulse函数求解分数阶Lane-Emden微分方程
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作者 黄英杰 周凤英 许小勇 《数值计算与计算机应用》 2023年第1期95-112,共18页
基于第六类正交Chebyshev多项式混合Block-Pulse函数,获得了一种求解分数阶Lane-Emden型微分方程数值解的数值方法.混合函数由第六类正交Chebyshev多项式与Block-Pulse函数构成.在Rieman-Liouville分数阶积分定义下,利用Laplace变换导... 基于第六类正交Chebyshev多项式混合Block-Pulse函数,获得了一种求解分数阶Lane-Emden型微分方程数值解的数值方法.混合函数由第六类正交Chebyshev多项式与Block-Pulse函数构成.在Rieman-Liouville分数阶积分定义下,利用Laplace变换导出了混合函数的分数阶积分公式表达式.利用混合函数积分公式以及结合有效的配点法,将具有边界条件的分数阶Lane-Emden微分方程转化成一个代数方程组,再运用迭代法进行数值求解.同时,还给出了混合函数展开的一致收敛性分析和误差估计.文中数值算例和数值结果验证了该方法的有效性和准确性. 展开更多
关键词 分数阶Lane-Emden微分方程 第六类正交Chebyshev多项式 block-pulse函数 Rieman-Liouville分数阶积分
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Numerical solution of fractional Mathieu equations by using block-pulse wavelets 被引量:1
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作者 P.Pirmohabbati A.H.Refahi Sheikhani +1 位作者 H.Saberi Najafi A.Abdolahzadeh Ziabari 《Journal of Ocean Engineering and Science》 SCIE 2019年第4期299-307,共9页
In this paper,we introduce a method based on operational matrix of fractional order integration for the numerical solution of fractional Mathieu equation and then apply it in a number of cases.For this,we use the bloc... In this paper,we introduce a method based on operational matrix of fractional order integration for the numerical solution of fractional Mathieu equation and then apply it in a number of cases.For this,we use the block-pulse wavelets matrix of fractional order integration with respect to the Caputo sense.The method was tested by some numerical examples and changes occurred in the coefficients as well as in the derivative of the equation.Results prove the accuracy and computational efficiency of the proposed algorithm.©2019 Shanghai Jiaotong University.Published by Elsevier B.V. 展开更多
关键词 block-pulse functions Fractional calculus Mathieu differential equation
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二维Volterra-Fredholm积分方程数值算法研究及收敛性分析 被引量:1
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作者 解加全 刘霄琪 张佳乐 《工程数学学报》 CSCD 北大核心 2022年第6期1012-1020,共9页
针对一类二维非线性Volterra-Fredholm积分方程,提出利用二维Block-Pulse函数为基函数进行数值求解。首先,引入Block-Pulse函数的定义及基函数的向量表示形式;其次,根据二维Block-Pulse函数的不相交性和正交性推导了基向量的积分算子矩... 针对一类二维非线性Volterra-Fredholm积分方程,提出利用二维Block-Pulse函数为基函数进行数值求解。首先,引入Block-Pulse函数的定义及基函数的向量表示形式;其次,根据二维Block-Pulse函数的不相交性和正交性推导了基向量的积分算子矩阵和乘积算子矩阵;然后,基于该算子矩阵将待求问题转化为一系列向量的乘积形式,利用配点法离散未知变量获得原问题的数值解;最后,通过两个具体的数值算例对所提算法的可行性和收敛性进行了验证。 展开更多
关键词 Volterra-Fredholm积分方程 二维block-pulse函数 算子矩阵 数值解 收敛性
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Numerical Solution of Nonlinear Fredholm-Volterra Integtral Equations via Piecewise Constant Function by Collocation Method 被引量:1
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作者 A. Shahsavaran 《American Journal of Computational Mathematics》 2011年第2期134-138,共5页
In this work, we present a computational method for solving nonlinear Fredholm-Volterra integral equations of the second kind which is based on replacement of the unknown function by truncated series of well known Blo... In this work, we present a computational method for solving nonlinear Fredholm-Volterra integral equations of the second kind which is based on replacement of the unknown function by truncated series of well known Block-Pulse functions (BPfs) expansion. Error analysis is worked out that shows efficiency of the method. Finally, we also give some numerical examples. 展开更多
关键词 NONLINEAR Fredholm-Volterra Integral Equation block-pulse FUNCTION Error Analysis COLLOCATION Points
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Solution of Multi-Delay Dynamic Systems by Using Hybrid Functions
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作者 K. Maleknejad R. Ezzati T. Damercheli 《Applied Mathematics》 2014年第13期2016-2027,共12页
In this paper, we present a method for finding the solution of the linear multi-delay systems (MDS) by using the hybrid of the Block-Pulse functions and the Bernoulli polynomials. In this approach, the MDS is reduced ... In this paper, we present a method for finding the solution of the linear multi-delay systems (MDS) by using the hybrid of the Block-Pulse functions and the Bernoulli polynomials. In this approach, the MDS is reduced to a system of linear algebraic equations by expanding various time functions for the hybrid functions and using operational matrices. To demonstrate the validity and the applicability of the technique, some examples are presented. 展开更多
关键词 block-pulse FUNCTIONS BERNOULLI POLYNOMIALS Multi-Delay SYSTEMS
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