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

Nadir M.

Journal of Theoretical and Applied Computer Science

2016

Vol. 10, nr 1

19--25

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)

Adapted quadratic approximation for logarithmic kernel integrals

Nadir M.

Fasciculi Mathematici

2012

Nr 49

75--85

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.