4 results for “singular integral equations”

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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 titleOn the General Solution of First-Kind Hypersingular Integral EquationsSuzan J. Obaiys, Z. Abbas, N. M.A. Nik Long et al.A new algorithm is presented to provide a general solution for a first type Hyper singular Integral Equation (HSIE). The singular integral has been converted into a regular form by cancelling the singularity and then transforming it into a system of algebraic equation based orthogonal poly- nomials. We applied the convergence method presented by (Obaiys, 2013) to conform the numerical … …American Journal of Engineering and Applied Sciences, Vol. 9, Issue 2 · 28 Jan 2016 · 8,699 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsQuadratic 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

Research ArticleOpen accessIn the keywordsA 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