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On the Convergence Problem of One-Dimensional Hypersingular Integral Equations

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  • Suzan J. Obaiys

Abstract

We develop the expansion method of singular integral equation (SIE) for hypersingular integral equation (HSIE). Relating the hypersingular integrals to Cauchy principal-value integrals, we interpolate the kernel and the density functions to the truncated Chebyshev series of the second kind. The corresponding convergence results for the functions and , , are derived in an appropriate norm to the true solution of the weight function. Numerical examples are also presented to validate the theoretical findings.

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  • Suzan J. Obaiys, 2013. "On the Convergence Problem of One-Dimensional Hypersingular Integral Equations," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-6, December.
    • Handle: RePEc:hin:jnlmpe:974751
    DOI: 10.1155/2013/974751
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