Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equations

Yazdani, S.; Hadizadeh, M.

doi:10.1590/s1807-03022012000200005

Cited by 2 publications

(1 citation statement)

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“…The collocation methods for nonlinear Volterra-Fredholm integral equations were investigated in [6]. In [19] piecewise constant bounds on the solution of mixed nonlinear Volterra-Fredholm integral equations were presented. Guoqiang [9] introduced and discussed the asymptotic error expansion of a collocation-type method for Volterra-Hammerstein integral equations and a collocationtype method was developed in [12].…”

Section: B Sepehrian and M Razzaghimentioning

confidence: 99%

A New Method for Solving Nonlinear Volterra-Hammerstein Integral Equations Via Single-Term Walsh Series

Sepehrian

Razzaghi

2020

MACO

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In this article, the properties of single-term Walsh series are presented and utilized for solving the nonlinear Volterra-Hammerstein integral equations of second kind. The interval [0, 1) is divided to m equal subintervals, m is a positive integer number. The midpoint of each subinterval is chosen as a suitable collocation point. By the method the computations of integral equations reduce into some nonlinear algebraic equations. The method is computationally attractive, and gives a continuous approximate solution. An analysis for the convergence of method is presented. The efficiency and accuracy of the method are demonstrated through illustrative examples. Some comparisons are made with the existing results.

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Section: B Sepehrian and M Razzaghimentioning

confidence: 99%

A New Method for Solving Nonlinear Volterra-Hammerstein Integral Equations Via Single-Term Walsh Series

Sepehrian

Razzaghi

2020

MACO

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Solving Two-dimensional Linear Volterra-Fredholm Integral Equations of the Second Kind by Using Series Solution Methods

Saeed¹,

Berdawood²

2015

JZS

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In this paper, we focus on obtaining an approximate solution of the two types of two- dimensional linear Volterra-Fredhom integral equations of the second kind. Series solution method is reformulated and applied with different bases functions for finding an approximate solution (sometimes the exact solution) for the above two types of integral equations. This is done by computer program with the aid of the Maple code program version 13 for all the above prescribed methods. Furthermore, we proved some theoretical results on the convergence analysis of the presented methods.

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Piecewise constant bounds for the solution of nonlinear Volterra-Fredholm integral equations

Abstract: Abstract.In this paper, we compute piecewise constant bounds on the solution of mixed Mathematical subject classification: 65G20, 45G10, 65G40.

Cited by 2 publications

References 20 publications

A New Method for Solving Nonlinear Volterra-Hammerstein Integral Equations Via Single-Term Walsh Series

A New Method for Solving Nonlinear Volterra-Hammerstein Integral Equations Via Single-Term Walsh Series

Solving Two-dimensional Linear Volterra-Fredholm Integral Equations of the Second Kind by Using Series Solution Methods

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