Solution of multi-delay systems using hybrid of block-pulse functions and Taylor series

Marzban, Hamid Reza; Razzaghi, Mohsen

doi:10.1016/j.jsv.2005.08.007

Cited by 71 publications

(38 citation statements)

References 10 publications

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“…2 and 3. Also, the exact solution for the delay system obtained by the presented method is compared with other methods since hybrid of block pulse functions and Taylor series (b nm (t), n = 1, · · · , N, m = 0, 1, · · · , M − 1) [18], where n and m are the order of block pulse functions and Taylor polynomials, respectively. Here is the solution of this example obtained with hybrid functions by choosing N = 3 and M = 7.…”

Section: Illustrative Examplesmentioning

confidence: 99%

Solution of linear time-varying multi-delay systems via variational iteration method

Mirhosseini-Alizamini¹,

Effati²,

Heydari³

2016

J. Math. Computer Sci.

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This work presents an approximate solution method for the linear time-varying multi-delay systems and time delay logistic equation using variational iteration method. The method is based on the use of Lagrange multiplier for identification of optimal value of a parameter in a functional. This procedure is a powerful tool for solving large amount of problems. Also, it provides a sequence which converges to the solution of the problem without discretization of the variables. In this study, an idea is proposed that accelerates the convergence of the sequence which results from the variational iteration formula for solving systems of delay differential equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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Section: Illustrative Examplesmentioning

confidence: 99%

Solution of linear time-varying multi-delay systems via variational iteration method

Mirhosseini-Alizamini¹,

Effati²,

Heydari³

2016

J. Math. Computer Sci.

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“…For such kind of problem, the approach is that of converting the underlaying differential equations govering the dynamical system to an algebraic form through the use of an operational matrix of integration which can be uniquely determined based on the particular OFs. Special attentions have been given to applications of Walsh functions [7], block-pulse functions [8][9][10], Laguerre polynomials [11], Legendre polynomials [12][13][14], Chebyshev polynomials [15,16], Taylor series [17,18] and Fourier series [19,20].…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of Time Delay Systems via Hybrid of Block-Pulse Functions and Orthonormal Taylor Series

Dadkhah

Farahi

2015

Int. J. Appl. Comput. Math

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A new method to find the optimal control of time delay systems with quadratic performance index is discussed. The method is based on hybrid functions. The properties of the hybrid functions which consists of block-pulse functions and orthonormal Taylor series are presented. The operational matrices of integration, delay, dual and product are used to reduce the solution of optimal control time delay system to the solution of algebraic equations. Numerical examples are included to illustrate the effectiveness and validity of the technique.

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“…Maleknejad and Tavassoli Kajani in [25] introduced a Galerkin method based on hybrid Legendre and block-pulse functions on interval [0, 1) to solve the linear integrodifferential equation system. Razzaghi and Marzban in [26], a direct method for solving multidelay systems using hybrid of block-pulse functions and Taylor series is presented. Marzban et al [27] implemented hybrid of blockpulse functions and Lagrange-interpolating polynomials to find approximate solution of Volterra's population model.…”

Section: Introductionmentioning

confidence: 99%

Application of Hybrid Functions for Solving Duffing-Harmonic Oscillator

Heydari

Loghmani

Hosseini

et al. 2014

Journal of Difference Equations

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A numerical method for finding the solution of Duffing-harmonic oscillator is proposed. The approach is based on hybrid functions approximation. The properties of hybrid functions that consist of block-pulse and Chebyshev cardinal functions are discussed. The associated operational matrices of integration and product are then utilized to reduce the solution of a strongly nonlinear oscillator to the solution of a system of algebraic equations. The method is easy to implement and computationally very attractive. The results are compared with the exact solution and results from several recently published methods, and the comparisons showed proper accuracy of this method.

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Solution of multi-delay systems using hybrid of block-pulse functions and Taylor series

Cited by 71 publications

References 10 publications

Solution of linear time-varying multi-delay systems via variational iteration method

Solution of linear time-varying multi-delay systems via variational iteration method

Optimal Control of Time Delay Systems via Hybrid of Block-Pulse Functions and Orthonormal Taylor Series

Application of Hybrid Functions for Solving Duffing-Harmonic Oscillator

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