Using the WPG method for solving integral equations of the second kind

Maleknejad, K.; Karami, M.

doi:10.1016/j.amc.2004.04.109

Cited by 28 publications

(10 citation statements)

References 4 publications

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“…Next, we substitute these matrices in equation 11and then simplify to obtain which is the exact solution [5,8]. We give numerical analysis for 10 , 9 = N in Table 1 and Fig.…”

Section: Numerical Illustrationsmentioning

confidence: 99%

Legendre Series Solutions of Fredholm Integral Equations

Yalçınbaş

Aynigül

Akkaya

2010

MCA

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A matrix method for approximately solving linear Fredholm integral equations of the second kind is presented. The solution involves a truncated Legendre series approximation. The method is based on first taking the truncated Legendre series expansions of the functions in equation and then substituting their matrix forms into the equation. Thereby the equation reduces to a matrix equation, which corresponds to a linear system of algebraic equations with unknown Legendre coefficients. In addition, some equations considered by other authors are solved in terms of Legendre polynomials and the results are compared.

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“…Next, we substitute these matrices in equation 11and then simplify to obtain which is the exact solution [5,8]. We give numerical analysis for 10 , 9 = N in Table 1 and Fig.…”

Section: Numerical Illustrationsmentioning

confidence: 99%

Legendre Series Solutions of Fredholm Integral Equations

Yalçınbaş

Aynigül

Akkaya

2010

MCA

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“…Consider the second-kind linear Fredholm integral equation of the form the f (x) and K(x, t) are known functions and y(x) is the unknown function that is to be determined. This type of equations has been solved in many papers with many different methods [1][2][3][4][5][6]. Wavelet bases have been used recently which, primarily because of their local supports and vanishing moment properties, lead to a sparse matrix.…”

Section: Introductionmentioning

confidence: 99%

Low memory requirement and computational time method for solving a class of integral equations

Maleknejad

Sahlan

Torabi

2011

Procedia Computer Science

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In this work, we present a new low memory requirement and low computational time method for solving a class of integral equation of the second kind which is based on the use of B-Spline wavelets. Because of vanishing moments and compact support and semiorthogonality properties of these wavelets, operational matrix of the method is very sparse. Also, applying some appropriate thresholding parameter and GMRES method for solving sparse systems, we get a computationally attractive method with low CPU requirement. For showing the accuracy of the method some numerical method are presented.

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“…But the presented structures have the restriction that is a disadvantage. In [3][4][5]10,11,13,14] the mentioned disadvantage is removed by using multiwavelet schemes.…”

Section: Introductionmentioning

confidence: 99%