Wavelet Galerkin method for solving singular integral equations

Maleknejad, K.; Nosrati, Masoud S.; Najafi, Esmaeil

doi:10.1590/s1807-03022012000200009

Cited by 11 publications

(2 citation statements)

References 33 publications

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“…Then the rate is improved to O(n −m ) [14] which now depends on m, but still at polynomial order. Some numerical methods for solving weakly singular equations are; Bessel polynomials via collocation method [15], Clenshaw-Curtis-Filon quadrature [16], Laguerre functions [17], B-spline Wavelet Galerkin method [18], Block-pulse functions [19], Lagrange interpolation with Gauss Legendre quadrature nodes [20]. In this work we assume that the…”

Section: Introductionmentioning

confidence: 99%

Triangular functions in solving Weakly Singular Volterra integral equations

NOSRATİ¹,

Afshari

2023

Advances in the Theory of Nonlinear Analysis and Its Application

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In this paper, we propose the triangular orthogonal functions as a basis functions for solution of weakly singular Volterra integral equations of the second kind. Powerful properties of these functions and some operational matrices are utilized in a direct method to reduce singular integral equation to some algebraic equations. The presented method does not need any integration for obtaining the constant coefficients. The method is computationally attractive, and applications are demonstrated through illustrative examples.

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Section: Introductionmentioning

confidence: 99%

Triangular functions in solving Weakly Singular Volterra integral equations

NOSRATİ¹,

Afshari

2023

Advances in the Theory of Nonlinear Analysis and Its Application

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“…In [8], a generalization of the Euler-Maclaurin summation formula for solving WSFIEs of the second kind was introduced. One can refer to the methods that were proposed in [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Reproducing kernel method for a class of weakly singular Fredholm integral equations

Alvandi

Paripour

2018

Journal of Taibah University for Science

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Numerical methods for solving integral equations have been the focus of much research, including reproducing kernel methods. We present a new algorithm to solve weakly singular Fredholm integral equations (WSFIEs). The advantage of this method is that it is possible to pick any point in the interval of integration and also the approximate solution. The advantage of this method is used to remove singularity and reproducing kernel functions are used as a basis. The convergence of approximation solution to the exact solution is also proved. Some examples are displayed to demonstrate that the method is accurate and efficient for WSFIEs.

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Bivariate Jacobi polynomials for solving Volterra partial integro‐differential equations with the weakly singular kernel

Sadri

Hosseini

Mirzazadeh

et al. 2021

Math Methods in App Sciences

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An operational matrix method is implemented based on the bivariate Jacobi polynomials to attain numerical solutions of a category of Volterra weakly singular partial integro‐differential equations (VWSPI‐DEs). Utilizing Jacobi approximations and their integral, derivative, and pseudo‐integral operational matrices along with the collocation method reduces the given VWSPI‐DE to a system of algebraic equations. Diverse forms of the Jacobi polynomials are used to investigate and compare errors of obtained approximate solutions. Moreover, some error bounds are computed for the error functions. Four experimental illustrations are solved to exhibit the effectiveness and suitability of the proposed scheme.

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Wavelet Galerkin method for solving singular integral equations

Cited by 11 publications

References 33 publications

Triangular functions in solving Weakly Singular Volterra integral equations

Triangular functions in solving Weakly Singular Volterra integral equations

Reproducing kernel method for a class of weakly singular Fredholm integral equations

Bivariate Jacobi polynomials for solving Volterra partial integro‐differential equations with the weakly singular kernel

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