Numerical solution of nonlinear Volterra–Fredholm–Hammerstein integral equations via collocation method based on radial basis functions

Parand, Kourosh; Rad, Jamal Amani

doi:10.1016/j.amc.2011.11.013

Cited by 67 publications

(30 citation statements)

References 65 publications

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“…The given results suggest that using the present approach leads to acceptable results in comparison with different approximation methods. Finally, we note that the proposed method can be applied to a large class of nonlinear and linear partial differential equations [56 -58], ordinary differential equations [59], and integral equations [60,61] in finite or infinite domain.…”

Section: Discussionmentioning

confidence: 99%

A new Reliable Numerical Algorithm Based on the First Kind of Bessel Functions to Solve Prandtl–Blasius Laminar Viscous Flow over a Semi-Infinite Flat Plate

Parand

Nikarya

Rad

et al. 2012

Zeitschrift Für Naturforschung A

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In this paper, a new numerical algorithm is introduced to solve the Blasius equation, which is a third-order nonlinear ordinary differential equation arising in the problem of two-dimensional steady state laminar viscous flow over a semi-infinite flat plate. The proposed approach is based on the first kind of Bessel functions collocation method. The first kind of Bessel function is an infinite series, defined on R and is convergent for any x ∈ R. In this work, we solve the problem on semi-infinite domain without any domain truncation, variable transformation basis functions or transformation of the domain of the problem to a finite domain. This method reduces the solution of a nonlinear problem to the solution of a system of nonlinear algebraic equations. To illustrate the reliability of this method, we compare the numerical results of the present method with some well-known results in order to show the applicability and efficiency of our method.

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Section: Discussionmentioning

confidence: 99%

A new Reliable Numerical Algorithm Based on the First Kind of Bessel Functions to Solve Prandtl–Blasius Laminar Viscous Flow over a Semi-Infinite Flat Plate

Parand

Nikarya

Rad

et al. 2012

Zeitschrift Für Naturforschung A

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“…For more references about numerical methods for Volterra-Hammerstein integral equations ( see e.g. [7][8][9]19], etc).…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of nonlinear Volterra–Fredholm–Hammerstein integral equations via Tau-collocation method with convergence analysis

Gouyandeh

Allahviranloo

Armand

2016

Journal of Computational and Applied Mathematics

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Please cite this article as: Z. Gouyandeh, T. Allahviranloo, A. Armand, Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via Tau-collocation method with convergence analysis, Journal of Computational and Applied Mathematics (2016), http://dx. AbstractIn this paper, we consider the nonlinear Volterra-Fredholm-Hammerstein integral equations. The approximate solution for the nonlinear Volterra-Fredholm-Hammerstein integral equations is obtained by using the Tau-Collocation method. To do this, the nonlinear Volterra-Fredholm-Hammerstein integral equations is transformed into a system of nonlinear algebraic equations in matrix form. Thus by solving this system unknown coefficients are obtained. The spectral rate of convergence for the proposed method is established in the L 2 -norm. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the Tau-collocation method is of high accuracy, more convenient and efficient for solving nonlinear Volterra-Fredholm-Hammerstein integral equations.

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“…And many methods have been proposed for solving them such as modified decomposition method [2,3], reproducing kernel Hilbert space method [4], Legendre wavelets method [5], homotopy perturbation method [6], a composite collocation method [7], rationalized Haar functions method [8], variational iteration method [9], collocation method based on radial basis functions [10], method based on Bernstein operational matrices [11], hybrid of block-pulse functions and Taylor series method [12], sinc method [13] etc. The comprehensive view of nonlinear Volterra-Fredholm integral equations can be found in Ref.…”

Section: Introductionmentioning

confidence: 99%

An efficient algorithm for solving nonlinear Volterra–Fredholm integral equations

Zhong

Jiang

2015

Applied Mathematics and Computation

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Numerical solution of nonlinear Volterra–Fredholm–Hammerstein integral equations via collocation method based on radial basis functions

Cited by 67 publications

References 65 publications

A new Reliable Numerical Algorithm Based on the First Kind of Bessel Functions to Solve Prandtl–Blasius Laminar Viscous Flow over a Semi-Infinite Flat Plate

A new Reliable Numerical Algorithm Based on the First Kind of Bessel Functions to Solve Prandtl–Blasius Laminar Viscous Flow over a Semi-Infinite Flat Plate

Numerical solution of nonlinear Volterra–Fredholm–Hammerstein integral equations via Tau-collocation method with convergence analysis

An efficient algorithm for solving nonlinear Volterra–Fredholm integral equations

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