Numerical Simulation of Fractional Control System Using Chebyshev Polynomials

Jun, Zhang; Li, Yugui; Xie, Jiaquan

doi:10.1155/2018/4270764

Cited by 4 publications

(5 citation statements)

References 26 publications

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“…Hongchun et al [33] presented meshless barycentric interpolation collocation technique for finding the solution of PDEs which are encountered in many physical problems. Zhang et al [34] presented numerical technique for fraction control problems using Chebyshev polynomials. Yao et al [35] developed a mathematical model for investigating the loss of root stone due water flow in dam structure.…”

Section: Introductionmentioning

confidence: 99%

Numerical Treatment for the Three-Dimensional Eyring-Powell Fluid Flow over a Stretching Sheet with Velocity Slip and Activation Energy

Umar

Akhtar

Sabir

et al. 2019

Advances in Mathematical Physics

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In this manuscript, a computational paradigm of technique shooting is exploited for investigation of the three-dimensional Eyring-Powell fluid with activation energy over a stretching sheet with slip arising in the field of fluid dynamics. The problem is modeled and resulting nonlinear system of PDEs is transformed into nonlinear system of ODEs using well-known similarity transformations. The strength of shooting based computing approach is employed to analyze the dynamics of the system. The proposed technique is well-designed for different scenarios of the system based on three-dimensional non-Newtonian fluid with activation energy over a stretching sheet. Slip condition is also incorporated to enhance the physical and dynamical analysis of the system. The proposed results are compared with the bvp4C method for the correctness of the solver. Graphical and numerical illustrations are used to envisage the behavior of different proficient physical parameters of interest including magnetic parameter, stretching rate parameter, velocity slip parameter, Biot number on velocity, and Lewis number on temperature and concentration.

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Section: Introductionmentioning

confidence: 99%

Numerical Treatment for the Three-Dimensional Eyring-Powell Fluid Flow over a Stretching Sheet with Velocity Slip and Activation Energy

Umar

Akhtar

Sabir

et al. 2019

Advances in Mathematical Physics

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“…On the other hand, some systems, such as the integral equations [17,18], which were based on the operational matrices of integration, were estimated using polynomials. These included block pulse systems, the Fourier series, Legendre polynomials, Chebyshev polynomials, and Laguerre polynomials.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution for stochastic Volterra-Fredholm integral equations with delay arguments

Yao,

Zhang,

Shi

2024

Acta Polytech

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We present a method for computing the stochastic operational matrix of integration to advance the study of stochastic Volterra-Fredholm integral equations (SVFIEs) based on delay arguments. First, the method evaluates the combined effects of the delay and its parameters on the accuracy improvement of the convergence rate. Our results can be applied to SVFIEs, with the operational delay matrices of the block pulse function simplified to algebraic ones. Numerical calculations were performed on a PC using Python 3 programs. Results also demonstrate the accuracy of approximate solutions; arithmetic operations are carried out without the need for derivation or integration.

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“…Different Volterra integral equations are handled by Bernstein polynomials, block pulse functions, least squares method, Haar wavelets, Walsh functions, Chebyshev and Legendre polynomials, and other functions. We only mentioned the referenced such as [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and other relevant literatures. On the other hand, some authors obtained the numerical solution of stochastic Volterra integral equation by Euler-Maruyama approximation or iterative algorithm, for example [22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

“…m � 24 , the approximate solution and exact solution for Example 1m � 25 , the approximate solution and exact solution for Example 1.…”

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confidence: 99%

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Numerical Solution of Multidimensional Stochastic Itô-Volterra Integral Equation Based on the Least Squares Method and Block Pulse Function

Jiang

Deng

2021

Mathematical Problems in Engineering

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In this paper, a method based on the least squares method and block pulse function is proposed to solve the multidimensional stochastic Itô-Volterra integral equation. The Itô-Volterra integral equation is transformed into a linear algebraic equation. Furthermore, the error analysis is given by the isometry property and Doob’s inequality. Numerical examples verify the effectiveness and precision of this method.

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Numerical Simulation of Fractional Control System Using Chebyshev Polynomials

Cited by 4 publications

References 26 publications

Numerical Treatment for the Three-Dimensional Eyring-Powell Fluid Flow over a Stretching Sheet with Velocity Slip and Activation Energy

Numerical Treatment for the Three-Dimensional Eyring-Powell Fluid Flow over a Stretching Sheet with Velocity Slip and Activation Energy

Numerical solution for stochastic Volterra-Fredholm integral equations with delay arguments

Numerical Solution of Multidimensional Stochastic Itô-Volterra Integral Equation Based on the Least Squares Method and Block Pulse Function

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