Bezier Curves for Solving Fredholm Integral Equations of the Second Kind

Ghomanjani, Fateme; Farahi, Mohammad Hadi; Kılıçman, Adem

doi:10.1155/2014/147497

Mathematical Problems in Engineering

2014

DOI: 10.1155/2014/147497

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Bezier Curves for Solving Fredholm Integral Equations of the Second Kind

Fateme Ghomanjani

Mohammad Hadi Farahi

Adem Kılıçman

Abstract: The Bezier curves are presented to estimate the solution of the linear Fredholm integral equation of the second kind. A direct algorithm for solving this problem is given. We have chosen the Bezier curves as piecewise polynomials of degreenand determine Bezier curves on [0, 1] byn+1control points. Numerical examples illustrate that the algorithm is applicable and very easy to use.

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“…Bezier functions were applied for solving Fredholm integral equations (see [14,15,16]), Volterra integral equations [17], and Volterra-Fredholm-Hammerstein integral equations [18]. Zheng et al [19] and Safaie and Copyright © 2020 MECS I.J.…”

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confidence: 99%

A Novel Method to Solve a Class of Non-local Diffusion Optimal Control Problems by using Bernstein Polynomials

Ketabdari¹,

Farahi²

2020

IJISA

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The aim of this paper is solving optimal control problems governed by non-local diffusion equations via a mesh-less method. The diffusion equation and in particular, the heat conduction equation is essential in sciences. This equation appears in many fields, such as engineering, electrostatic, and mathematics. For solving the mentioned optimal control problems, the method is established upon expanding of variables by the basis of Bezier functions. We apply, for the first time, the Bernstein approximation in solving an optimal control problem governed by the diffusion equation. A direct algorithm is given for solving this problem. Bernstein polynomials expand the trajectories and control functions with unknown control points. Then the optimal control problem is converted to a mathematical programming problem. By solving the mathematical programming problem, the approximated solution of trajectories and control are driven. The convergence of the method in approximating of the optimal control problem is proved. Some numerical examples for demonstrating the effectiveness of the method are included.

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confidence: 99%

A Novel Method to Solve a Class of Non-local Diffusion Optimal Control Problems by using Bernstein Polynomials

Ketabdari¹,

Farahi²

2020

IJISA

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Bezier Curves for Solving Fredholm Integral Equations of the Second Kind

Cited by 1 publication

References 31 publications

A Novel Method to Solve a Class of Non-local Diffusion Optimal Control Problems by using Bernstein Polynomials

A Novel Method to Solve a Class of Non-local Diffusion Optimal Control Problems by using Bernstein Polynomials

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