Wavelet Galerkin method for numerical solution of nonlinear integral equation

Mahmoudi, Yaghoub

doi:10.1016/j.amc.2004.08.004

Cited by 49 publications

(25 citation statements)

References 4 publications

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“…Haar wavelet is the simplest example of wavelet but it is not smooth. In the past few years many authors have studied approximate solution of Fredholm integral equation of the second kind using wavelets; see [10,11,12,13]. Authors have used Haar wavelets, multiwavelets and B-spline wavelets.…”

Section: Introductionmentioning

confidence: 99%

An Approximate Solution of Fredholm Integral Equation of the Second Kind by Band-Limited Scaling Function

Priyadarshi¹,

Kumar²

2016

Int. J. of Pure and Appl. Math.

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Fredholm integral equation of the second kind appears naturally in different areas of mathematics, physics and engineering. In this paper we consider Fredholm integral equation of the second kind with convolution type kernel. We assume f in the approximation space and prove the existence and uniqueness of approximate solution by band-limited scaling function.Since these functions are infinitely differentiable and possess decay property, methods based on these functions would be very accurate. Convergence analysis has been discussed to validate our approximate solution.

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Section: Introductionmentioning

confidence: 99%

An Approximate Solution of Fredholm Integral Equation of the Second Kind by Band-Limited Scaling Function

Priyadarshi¹,

Kumar²

2016

Int. J. of Pure and Appl. Math.

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“…In recent publications, different mathematical tools and numerical implementations have been applied to solve integral equations (1). In some of these publications, certain authors extensively use methods based on different kinds of wavelets [4,5]. Polynomial approximation methods using different base functions, such as Chebyshev polynomials, have been introduced; see for example [6,7].…”

Section: Introductionmentioning

confidence: 99%

On the Existence of Solutions of Nonlinear Fredholm Integral Equations from Kantorovich’s Technique

Ezquerro¹,

Hernández‐Verón²

2017

Algorithms

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Abstract:The well-known Kantorovich technique based on majorizing sequences is used to analyse the convergence of Newton's method when it is used to solve nonlinear Fredholm integral equations. In addition, we obtain information about the domains of existence and uniqueness of a solution for these equations. Finally, we illustrate the above with two particular Fredholm integral equations.Keywords: Fredholm integral equation; Newton's method; convergence; Kantorovich's technique; domain of existence of a solution; domain of uniqueness of a solution.

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“…Haar wavelet method with operational matrices of integration [15] has been applied to solve system of linear Fredholm integral equations of second kind. Quadrature method [16], B-spline wavelet method [17], wavelet Galerkin method [18], and also VIM [19] can be applied to solve nonlinear Fredholm integral equation of second kind. Some iterative methods like Homotopy perturbation method (HPM) [20][21] and Adomian decomposition method (ADM) [22] have been applied to solve nonlinear Fredholm integral equation of second kind.…”

Section: Introductionmentioning

confidence: 99%

An efficient hybrid method for solving fredholm integral equations using triangular functions

Ali¹,

Ramadan²

2017

ntmsci

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Abstract:In this paper the orthogonal triangular function (TF) based method is first applied to transform the Fredholm integral equations and Fredholm system of integral equations to a coupled system of matrix algebraic equations. The obtained system is a variant of coupled Sylvester matrix equations. A finite iterative algorithm is then applied to solve this system to obtain the coefficients used to get the form of approximate solution of the unknown functions of the integral problems. Some numerical examples are solved to illustrate the accuracy and the efficiency of the proposed hybrid method. The obtained numerical results are compared with other numerical methods and the exact solutions.

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Wavelet Galerkin method for numerical solution of nonlinear integral equation

Cited by 49 publications

References 4 publications

An Approximate Solution of Fredholm Integral Equation of the Second Kind by Band-Limited Scaling Function

An Approximate Solution of Fredholm Integral Equation of the Second Kind by Band-Limited Scaling Function

On the Existence of Solutions of Nonlinear Fredholm Integral Equations from Kantorovich’s Technique

An efficient hybrid method for solving fredholm integral equations using triangular functions

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