Numerical solutions of integrodifferential systems by hybrid of general block-pulse functions and the second Chebyshev polynomials

Wang, Xing Tao; Li, Yuan Min

doi:10.1016/j.amc.2008.12.044

Cited by 21 publications

(13 citation statements)

References 11 publications

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“…In recent years the hybrid functions consisting of the combination of block-pulse functions with Chebyshev polynomials [14][15][16], Legendre polynomials [17][18][19][20], or Taylor series [21,22] have been shown to be a mathematical power tool for discretization of selected problems. Among these three hybrid functions, the hybrid functions of block-pulse and Legendre polynomials have shown to be computationally more effective.…”

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confidence: 99%

Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

Haddadi

Ordokhani

Razzaghi

2011

J Optim Theory Appl

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In this paper, a new numerical method for solving the optimal control of linear time-varying delay systems with quadratic performance index is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions, consisting of block-pulse functions and Bernoulli polynomials, are presented. The operational matrices of integration, product, delay and the integration of the cross product of two hybrid functions of block-pulse and Bernoulli polynomials vectors are given. These matrices are then utilized to reduce the solution of the optimal control of delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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confidence: 99%

Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

Haddadi

Ordokhani

Razzaghi

2011

J Optim Theory Appl

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“…In recent years the hybrid functions consisting of the combination of blockpulse functions with Chebyshev polynomials [3], [4] Legendre polynomials [5], [6] or Taylor series [7], [8] have been shown to be a mathematical power tool for discretization of selected problems.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Functions for Nonlinear Differential Equations with Applications to Physical Problems

Razzaghi

2013

Lecture Notes in Computer Science

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Abstract.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 functions of block-pulse functions and Bernoulli polynomials are presented and are utilized to reduce the computation of nonlinear initialvalue problems to a system of equations. The method is easy to implement and yields very accurate results.

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“…Also many other hybrid functions have been used to solve integral equations. Hybrid Block-Pulse functions and the second Chebyshev polynomials [14] have been used to solve system of integro-differential equations. In [8], hybrid orthonormal Bernstein and Block-Pulse functions have been applied to solve the Fredholm integral equations.…”

Section: Introductionmentioning

confidence: 99%