Barycentric interpolation collocation methods for solving linear and nonlinear high-dimensional Fredholm integral equations

Liu, Hongyan; Huang, Jin; Pan, Yuyang; Zhang, Jipei

doi:10.1016/j.cam.2017.06.004

Cited by 47 publications

(24 citation statements)

References 25 publications

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“…The barycentric rational collocation method has been proved to be effective to solve non-linear high-dimensional Fredholm integral equations of the second kind [10] and non-linear parabolic partial differential equations [11].…”

Section: Introductionmentioning

confidence: 99%

The barycentric rational interpolation collocation method for boundary value problems

Tian

2018

THERM SCI

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Section: Introductionmentioning

confidence: 99%

The barycentric rational interpolation collocation method for boundary value problems

Tian

2018

THERM SCI

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“…Barycentric interpolation collocation method [16,17] is a high precision method. Some authors have used barycentric interpolation collocation method to solve various kinds of problems [16][17][18][19][20][21][22][23]. This paper suggests the barycentric interpolation collocation method to solve a class of hyperchaotic system, and a hyperchaotic system (1) is adopted as an example to elucidate the solution process.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of a Class of Hyperchaotic System Using Barycentric Lagrange Interpolation Collocation Method

Zhou

Wang

et al. 2019

Complexity

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Hyperchaotic system, as an important topic, has become an active research subject in nonlinear science. Over the past two decades, hyperchaotic system between nonlinear systems has been extensively studied. Although many kinds of numerical methods of the system have been announced, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, this paper introduces another novel numerical method to solve a class of hyperchaotic system. Barycentric Lagrange interpolation collocation method is given and illustrated with hyperchaotic system (x˙=ax+dz-yz,y˙=xz-by, 0≤t≤T,z˙=cx-z+xy,w˙=cy-w+xz,) as examples. Numerical simulations are used to verify the effectiveness of the present method.

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“…Berrut et al employed two versions of quadrature methods based on the linear BRI for the solution of Volterra integral equations of the second kind. Also, two CMs based on the barycentric Lagrange and the barycentric rational interpolants to identify approximate solutions of the high‐dimensional Fredholm integral equation are presented in Liu et al Rezaei et al used the quasi‐linearization method based on the barycentric Lagrange interpolation to find the approximate solution of fin problems. Torkaman et al proposed a new CM using the linear BRI to solve some nonlinear heat transfer problems.…”

Section: Introductionmentioning

confidence: 99%

Barycentric rational interpolation method for numerical investigation of magnetohydrodynamics nanofluid flow and heat transfer in nonparallel plates with thermal radiation

Torkaman

Heydari

Loghmani

et al. 2019

Heat Trans. Asian Res.

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In this study, the problem of heat transfer in the steady two-dimensional flow of an incompressible viscous magnetohydrodynamics nanofluid from a sink or source between two shrinkable or stretchable plates under the effect of thermal radiation has been studied. The governing differential equations have been solved numerically using a collocation method based on the barycentric rational basis functions. This method employs the derivative operational matrix of the barycentric rational bases and the weights that were introduced by Floater and Hormann. The influence of some embedding parameters, such as the solid volume fraction ϕ, the Reynolds number Re, the Hartmann number Ha, the Prandtl number Pr, the radiation parameter N , the stretching-shrinking parameter, C, and the angle of the channel α on the temperature distribution and velocity profile has been illustrated by graphs and tables. Numerical results reveal the efficiency and high accuracy of the proposed scheme compared to the previously existing solutions.Furthermore, the implementation of the proposed method is fast and the run time is short.linear barycentric rational interpolant, magnetohydrodynamic flow, nanofluid, operational matrix of derivative, stretchable or shrinkable walls, thermal radiation | INTRODUCTIONThe study of fluid flow between nonparallel plates is the focus of many research studies in the fields of engineering and science. This type of fluid flow is widely used in fluid mechanics, biomechanics, and electrical engineering. In the early 19th century, this kind of fluid flow, which is known as the Jeffrey-Hamel flow, was investigated by Jeffery 1 and Hamel. 2 The basic concept of magnetohydrodynamics (MHD) was first provided by Alfvén 3 in 1942, and it has important applications in engineering sciences, such as pumps, flow meters, MHD power generation, modeling of cooling systems based on liquid metals, and so on. [4][5][6][7] Most of the governing differential equations arising in engineering and physics are nonlinear, and, in most cases, it is not possible to obtain accurate and analytical solutions. Therefore, numerical or semianalytical techniques are utilized to solve such problems. Various numerical and semianalytical methods have been proposed for solving nonlinear problems arising in MHD nanofluid flow and heat transfer. In Esmaili et al, 8,9 the Adomian decomposition method is applied to obtain an approximate solution of the Jeffery-Hamel flow problem. Moghimi et al 10 used the homotopy perturbation method to solve the MHD Jeffery-Hamel flow problem. Also, Moghimi et al 11 employed the homotopy analysis method for the numerical solution of nonlinear MHD Jeffery-Hamel flows in nonparallel plates. Comparison between the HAM solutions and the numerical results based on fourth-fifth order Runge-Kutta (RKF45) method revealed the accuracy of this scheme. In Gerdroodbary et al, 12 the effect of thermal radiation on the classical Jeffery-Hamel flow has been studied numerically by using the collocation method (CM) and the least-square me...

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Barycentric interpolation collocation methods for solving linear and nonlinear high-dimensional Fredholm integral equations

Cited by 47 publications

References 25 publications

The barycentric rational interpolation collocation method for boundary value problems

The barycentric rational interpolation collocation method for boundary value problems

Numerical Simulation of a Class of Hyperchaotic System Using Barycentric Lagrange Interpolation Collocation Method

Barycentric rational interpolation method for numerical investigation of magnetohydrodynamics nanofluid flow and heat transfer in nonparallel plates with thermal radiation

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