3 articles for “Cauchy kernel”

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Research ArticleOpen accessPhrase in the titleHalf-bounded Numerical Solution of Singular Integral Equations with Cauchy KernelM. Abdulkawi, Z. K. Eshkuvatov, N.M.A. Nik LongProblem statement: In this study, a numerical solution for singular integral equations of the first kind with Cauchy kernel over the finite segment [-1,1] is presented. The numerical solution is bounded at x =1 and unbounded at x = -1. Approach: The numerical solution is derived by approximating the unknown density function using the weighted Chebyshev polynomials of the fourth … …Journal of Mathematics and Statistics, Vol. 7, Issue 1 · 25 Mar 2011 · 7,269 accessesView PDF Cite

Research ArticleOpen accessPhrase in the titleA Note on the Numerical Solution for Fredholm Integral Equation of the Second Kind with Cauchy kernelM. Abdulkawi, M.M.A. Nik Long, Z. K. EshkuvatovProblem statement: In this study, numerical solution for the Fredholm integral equation of the second kind with Cauchy singular kernel is presented. Approach: The Chebyshev polynomials of the second kind are used to approximate the unknown function. Results: Numerical results are given to show the accuracy of the present numerical solution. Conclusion: The present numerical solution to the Fredholm integral … …Journal of Mathematics and Statistics, Vol. 7, Issue 1 · 25 Mar 2011 · 7,677 accessesView PDF Cite

Research ArticleOpen accessIn the abstractQuadratic Approximation for Singular IntegralsMostefa NadirIn this study we present a new approach based on a quadratic approximation for singular integrals of Cauchy type, by using a small technical we arrive to eliminate completely the singularity of this integral. Noting that, this approximation is destined to solve numerically all singular integral equations with Cauchy kernel type on an oriented smooth contour. …Journal of Mathematics and Statistics, Vol. 8, Issue 2 · 4 Jul 2012 · 6,911 accessesView PDF Cite