Interactive Chebyshev–legendre Algorithm for Linear Quadratic Optimal Regulator Systems

Numerical treatments for the generalized Burger's—Huxley GBH equation are presented. The treatments are based on cardinal Chebyshev and Legendre basis functions with Galerkin method. Gauss quadrature formula and El-gendi method are used to convert the problem into a system of ordinary differential equations. The numerical results are compared with the literatures to show efficiency of the proposed methods.

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“…where ( )| = is the first-order differentiation matrix that depends on Legendre polynomial at the LGL nodes and has the entries given by [21]:…”

Section: El-gendi Legendre Galerkin (Elg) Methodsmentioning

confidence: 99%

Development of Galerkin Method for Solving the Generalized Burger's-Huxley Equation

El-Kady

El-Sayed

Fathy

2013

Mathematical Problems in Engineering

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“…Then equation (12) can be written as a system of ordinary differential equations (ODEs) in time as follows:…”

Section: Gauss Chebyshev Galerkin (Gcg) Methodsmentioning

confidence: 99%

“…On the other hand, the authors in [12] presented the error bound of the first and second order differentiation in equations (21) and (22), respectively, as follows:…”

Section: Errors In Differentiation Matricesmentioning

confidence: 99%

Chebyshev and Legendre via Galerkin method for solving KdV Burgers' equation

Fathy¹,

El-Kady²,

El-Sayed³

2013

ijcms

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In this paper, three numerical solutions for the Kortewegde Vries Burgers' (KdVB) equation are presented. Two of these methods are based on cardinal Chebyshev basis function with Galerkin method. Gauss-quadrature formula and El-gendi method are used to convert the problem into system of ordinary differential equations. In the third proposed method, the cardinal Legendre basis function with Galerkin method is used. In this case, the approximations are based on El-gendi method. The numerical results obtained by these ways have been compared with other solutions by Darvishi's preconditioning to the same problem to show the efficiency of the proposed methods.

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“…Table (3) shows that the presented Legendre approximations are more efficiency than the method in [16]. as given in [9]. Table ( 4) shows the state and control variables as computed by the proposed method.…”

Section: Examplementioning

confidence: 99%

“…See, for examp le, [7,9,11,14] and the references mentioned therein. A variety of numerical methods for solving infinite horizon variational optimal control problem exists in [15] and [18].…”

Section: Introductionmentioning

confidence: 99%

Legendre Approximations for Solving Optimal Control Problems Governed by Ordinary Differential Equations

El-Kady¹

2012

CONTROL

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In this paper Legendre integral method is proposed to solve optimal control problems governed by higher order ordinary differential equations. Legendre approximat ion method reduced the problem to a constrained optimizat ion problem. Penalty partial quadratic interpolation method is presented to solve the resulting constrained optimization problem. Error estimates for the Legendre appro ximations are derived and a technique that gives an optimal appro ximat ion of the problems is introduced. Numerical results are included to confirm the efficiency and accuracy of the method.

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Interactive Chebyshev–legendre Algorithm for Linear Quadratic Optimal Regulator Systems

Cited by 7 publications

References 14 publications

Development of Galerkin Method for Solving the Generalized Burger's-Huxley Equation

Development of Galerkin Method for Solving the Generalized Burger's-Huxley Equation

Chebyshev and Legendre via Galerkin method for solving KdV Burgers' equation

Legendre Approximations for Solving Optimal Control Problems Governed by Ordinary Differential Equations

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