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1

Lucas polynomials for solving linear integral equations

Nadir M.

Journal of Theoretical and Applied Computer Science

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2017

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Vol. 11, nr 1

13--19

EN

In this work, we seek the approximate solution of Fredholm and Volterra integral equations using Lucas polynomials and a given test functions, in order to reduce those equations to a linear system where its solution is to find the Lucas coefficients and thereafter the solution of the equation.The convergence of this method is assured and the error is compared with other methods.

2

Approximation solution for singular integral equations with logarithmic kernel using adapted linear spline

Nadir M.

Journal of Theoretical and Applied Computer Science

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2016

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Vol. 10, nr 1

19--25

EN

In this work, we apply a direct method for an approximative solution of a weakly singular integral equations (W.S.I.E) with logarithmic kernel on an oriented smooth contour using a modified linear spline approximation, we also show that this approximation gives an efficient approach to the analytical solution of (W.S.I.E)

3

A modified linear approximation for weakly singular integrals

Nadir M.

Journal of Theoretical and Applied Computer Science

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2015

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Vol. 9, nr 4

19--25

EN

In this work, we present a new approximation for a weakly singular integral, in particular Abel's integral. This approximation is based on the modification of the linear spline function, this one leads to eliminate the weak singularity. Noting that, it is clear that in the future we use this approximation for solving numerically all weakly singular integrals equations on an oriented smooth curve or on an interval.

4

A variational form with Bernoulli series for linear integral equations

Nadir M.

Journal of Theoretical and Applied Computer Science

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2014

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Vol. 8, nr 3

31--36

EN

In this work, we seek the approximate solution of Fredholm integral equations by truncation Bernoulli series approximation using a variational form for the equation. This one is reduced to a linear system where the solution of this latter gives the Bernoulli coefficients and thereafter the solution of the equation.The convergence and the error analysis of this method are discussed. Finally, we compare our numerical results by others.

5

Numerical solution of Hammerstein integral equations in Lp spaces

Nadir M., Gagui B

Fasciculi Mathematici

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2014

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Nr 52

83--91

EN

In this work, we give conditions guarantee the boundedness of the Hammerstein integral operator in Lp spaces. The existence and the uniqueness of the solution of Hammerstein integral equation are treated under some assumptions affected to the successive approximation, so that we obtain the convergence of the approximate solution to the exact one. Finally, we treat numerical examples to confirm our results.

6

Adapted quadratic approximation for logarithmic kernel integrals

Nadir M.

Fasciculi Mathematici

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2012

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Nr 49

75--85

EN

In this work, we explain a new numerical schemes of collocation methods based on the adapted quadratic approximation of singular integral with logarithmic kernel. This approximation leads to obtain the numerical solution of singular integral equations with logarithmic kernel on an oriented smooth contour.

7

On the numerical solution of singular integral equations using Sandikidze's approximaton

Nadir M., Antidze O. J.

Computational Methods in Science and Technology

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2004

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Vol. 10, nr 1

83-89

EN

The aim of this work is to solve singular integral equations (S.I.E), of Cauchy type on a smooth curve by pieces. This method is based on the approximation of the singular integral of the dominant part [6], where the (S.I.E) is reduced to a linear system of equations and to realize this approach numerically by the means of a program [3, 5].