Using the operational properties of general block-pulse functions and Legendre polynomials, the linear inverse time systems are transformed into a system of algebraic equations. The numerical solutions of the systems ...
详细信息
Using the operational properties of general block-pulse functions and Legendre polynomials, the linear inverse time systems are transformed into a system of algebraic equations. The numerical solutions of the systems are derived. Moreover, applying the results to the linear quadratic optimal control problems, the approximate solutions of optimal control of time delay systems are derived. (c) 2006 Elsevier Inc. All rights reserved.
In this paper two new recursive algorithms are presented for computing optimal control law of linear time-invariant singular systems with quadratic performance index by using the elegant properties of block-pulse func...
详细信息
In this paper two new recursive algorithms are presented for computing optimal control law of linear time-invariant singular systems with quadratic performance index by using the elegant properties of block-pulse functions (BPFs) and shifted Legendre polynomials (SLPs). Also a unified approach is given to solve the optimal control problem of singular systems via BPFs or SLPs. Two numerical examples are included to demonstrate the validity of the proposed algorithms and approach.
This paper presents a computational technique for the solution of the nonlinear mixed Volterra-Fredholm-Hammerstein integral equations. The method is based on the composite collocation method. The properties of hybrid...
详细信息
This paper presents a computational technique for the solution of the nonlinear mixed Volterra-Fredholm-Hammerstein integral equations. The method is based on the composite collocation method. The properties of hybrid of block-pulse functions and Lagrange polynomials are discussed and utilized to define the composite interpolation operator. The estimates for the errors are given. The composite interpolation operator together with the Gaussian integration formula are then used to transform the nonlinear mixed Volterra-Fredholm-Hammerstein integral equations into a system of nonlinear equations. The efficiency and accuracy of the proposed method is illustrated by four numerical examples. (C) 2010 Elsevier B.V. All rights reserved.
The aim of this paper is to present an efficient numerical procedure for solving the Abel's integral equation of the first and second kind and compare it with block-pulse functions (BPFs) method. The proposed meth...
详细信息
The aim of this paper is to present an efficient numerical procedure for solving the Abel's integral equation of the first and second kind and compare it with block-pulse functions (BPFs) method. The proposed method is based on Chebyshev wavelets approximation. This method transforms the integral equation into the matrix equation. The advantages of Chebyshev wavelets are that the values of mu(k) and M are adjustable as well as it can yield more accurate numerical solutions than piecewise constant orthogonal functions on the solution of integral equations. The uniform convergence theorem and accuracy estimation are derived and numerical examples show the validity and the wide applicability of the Chebyshev wavelets approach. (C) 2011 Ain Shams University. Production and hosting by Elsevier B.V. All rights reserved.
Most integral equations of the first kind are ill-posed, and obtaining their numerical solution often leads to solving a linear system of algebraic equations of a large condition number. So, solving this system is dif...
详细信息
Most integral equations of the first kind are ill-posed, and obtaining their numerical solution often leads to solving a linear system of algebraic equations of a large condition number. So, solving this system is difficult or impossible. For numerically solving Volterra integral equation of the first kind an efficient expansion-iterative method based on the block-pulse functions is proposed. Using this method, solving the first kind integral equation reduces to solving a recurrence relation. The approximate solution is most easily produced iteratively via the recurrence relation. Therefore, computing the numerical solution does not need to solve any linear system of algebraic equations. To show the convergence and stability of the method, some computable error bounds are obtained. Numerical examples are provided to illustrate that the method is practical and has good accuracy. (C) 2009 Elsevier Ltd. All rights reserved.
If we divide the interval [0, 1] into N sub-intervals, then hybrid Fourier and block-pulse functions on each sub-interval can approximate any function. This ability helps us to have more accurate approximations of pie...
详细信息
If we divide the interval [0, 1] into N sub-intervals, then hybrid Fourier and block-pulse functions on each sub-interval can approximate any function. This ability helps us to have more accurate approximations of piecewise continuous functions. Hence we obtain more accurate solutions to problems in the calculus of variations. In this article, we use a combination of Fourier and block-pulse functions on the interval [0, 1] to solve a variational problem in the solution of algebraic equations. An illustrative example is included to demonstrate the validity and applicability of the technique.
In this paper, the properties of the floor function has been used to find a function which is one on the interval [0, 1) and is zero elsewhere. The suitable dilation and translation parameters lead us to get similar f...
详细信息
In this paper, the properties of the floor function has been used to find a function which is one on the interval [0, 1) and is zero elsewhere. The suitable dilation and translation parameters lead us to get similar function corresponding to the interval [a, b). These functions and their combinations enable us to represent the stepwise functions as a function of floor function. We have applied this method on Haar wavelet, Sine-Cosine wavelet, block-pulse functions and Hybrid Fourier block-pulse functions to get the new representations of these functions. (c) 2009 Elsevier Inc. All rights reserved.
This paper endeavors to formulate block-pulse functions to propose solutions for the Fredholm integral equations system. To begin with we describe the characteristic of block-pulse functions and will go on to indicate...
详细信息
This paper endeavors to formulate block-pulse functions to propose solutions for the Fredholm integral equations system. To begin with we describe the characteristic of block-pulse functions and will go on to indicate that through this method a system of Fredholm integral equations can be reduced to an algebraic equation. Numerical examples presented to illustrate the accuracy of the method. (c) 2004 Elsevier Inc. All rights reserved.
A numerical method for solving nonlinear initial-value problems is proposed. The Lane-Emden type equations which have many applications in mathematical physics are then considered. The method is based upon hybrid func...
详细信息
A numerical method for solving nonlinear initial-value problems is proposed. The Lane-Emden type equations which have many applications in mathematical physics are then considered. The method is based upon hybrid function approximations. The properties of hybrid of block-pulse functions and Lagrange interpolating polynomials are presented and are utilized to reduce the computation of nonlinear initial-value problems to a system of non-algebraic equations. The method is easy to implement and yields very accurate results. (C) 2008 Published by Elsevier B.V.
A method for finding the optimal control of a linear time varying delay system with quadratic performance index is discussed. The properties of the hybrid functions which consists of block-pulse functions plus Chebysh...
详细信息
ISBN:
(纸本)9781889335384
A method for finding the optimal control of a linear time varying delay system with quadratic performance index is discussed. The properties of the hybrid functions which consists of block-pulse functions plus Chebyshev polynomials are presented. The operational matrices of integration, delay and product are then utilized to reduce the solution of optimal control to the solution of algebraic equations. An illustrative example is included to demonstrate the validity and applicability of the technique.
暂无评论