Numerical Solution for First Kind Fredholm Integral Equations by Using Sinc Collocation Method

Maleknejad, K.; Rostami, Yaser; Kalalagh, Hamed Shahi

doi:10.17706/ijapm.2016.6.3.120-128

Cited by 10 publications

(3 citation statements)

References 15 publications

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“…This equation has the exact solution u(x) = x. Table 1 compares our numerical results with those in [22]. We observe that the absolute errors obtained by our method at different values of M are better than obtained by the other method.…”

mentioning

confidence: 72%

“…In this section we are going to present some numerical experiments to check the applicability and accuracy of the method, also, we will test our results with some schemes appeared in previous papers by comparing them with the results in [19,20,[22][23][24]. All of the numerical calculations were carried out using Mathematica software.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Spectral Collocation Algorithm for Solving Fractional Volterra-Fredholm Integro-Differential Equations via Generalized Fibonacci Polynomials

Abo-Eldahab

Mohamed

Ali

2022

Contemporary Mathematics

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In this research article, we build and implement an efficient spectral algorithm for handling linear/nonlinear mixed Volterra-Fredholm integro-differential equations. First, we expand the exact solution as a truncated series of the generalized Fibonacci polynomials, and then we discretize the equation via Simpson's quadrature formula. Finally, we collocate the resulted residual at the roots of the shifted first-kind Chebyshev polynomials. Also, the rate of convergence is studied and the truncation error estimate is reported. Some numerical examples are exhibited to prove the applicability and accuracy of the algorithm.

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mentioning

confidence: 72%

Section: Numerical Examplesmentioning

confidence: 99%

Spectral Collocation Algorithm for Solving Fractional Volterra-Fredholm Integro-Differential Equations via Generalized Fibonacci Polynomials

Abo-Eldahab

Mohamed

Ali

2022

Contemporary Mathematics

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“…Maleknejad et al [103] proposed an advanced numerical model in solving the Fredholm integral equations of the first kind by using Sinc basis functions, Which method has been shown to be a powerful numerical solution for finding accurate solutions. Didgar et al [104] provide a new application of Taylor expansion approach for solving first kind Fredholm integral equations, wchich is based on employing the vth-degree Taylor polynomial of unknown function at an arbitrary point.…”

Section: Other Methodsmentioning

confidence: 99%

An overview of numerical methods for the first kind Fredholm integral equation

Zhang

2019

SN Appl. Sci.

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In the field of engineering technology, many problems can be transformed into the first kind Fredholm integral equation, which has a prominent feature called "ill-posedness". This property makes it difficult to find the analytical solution of first kind Fredholm integral equation. Therefore, how to find the numerical solution of first kind Fredholm integral equation has been a common concern of domestic and overseas scholars in recent years. In this article, various numerical solution methods of first kind Fredholm integral equation are introduced in detail. First, the existence and convergence of the solution of the integral equation are given. Second, the current mainstream numerical methods, such as regularization method, wavelet analysis method and multilevel iteration method are introduced in detail. Finally, we presented a concise overview of the numerical method of first kind Fredholm integral equation.

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A new Laguerre wavelets‐based method for solving Fredholm integral equations with weakly singular logarithmic kernel

Behera,

Ray

2024

Math Methods in App Sciences

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In this study, a wavelet‐based collocation scheme has been introduced for solving the linear and nonlinear Fredholm integral equations as well as the system of linear Fredholm integral equations with weakly singular logarithmic kernel. Initially, Laguerre wavelets have been constructed by dilation and translation of Laguerre polynomials. For the numerical solution of the Fredholm integral equations, all the functions have been approximated with respect to the Laguerre wavelets. Then, the proposed linear and nonlinear Fredholm integral equations reduce to systems of linear and nonlinear algebraic equations by utilizing the function approximations. Furthermore, the error estimation and the convergence analysis of the presented method have been discussed. Moreover, the numerical results of the several experiments have also been presented in both graphical and tabular form to describe the accuracy and efficiency of the approached method, and also, to determine the validity of the presented scheme, the approximate solutions and absolute error values are compared with the results obtained by other existing approaches.

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Numerical Solution for First Kind Fredholm Integral Equations by Using Sinc Collocation Method

Cited by 10 publications

References 15 publications

Spectral Collocation Algorithm for Solving Fractional Volterra-Fredholm Integro-Differential Equations via Generalized Fibonacci Polynomials

Spectral Collocation Algorithm for Solving Fractional Volterra-Fredholm Integro-Differential Equations via Generalized Fibonacci Polynomials

An overview of numerical methods for the first kind Fredholm integral equation

A new Laguerre wavelets‐based method for solving Fredholm integral equations with weakly singular logarithmic kernel

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