On the Convergence Problem of One-Dimensional Hypersingular Integral Equations

Abstract EN

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 f∈Cℓ([-1,1]) and K(t,x)∈Cℓ([-1,1]×[-1,1]), ℓ≥1, are derived in an appropriate L2[-1,1] norm to the true solution of the weight function.

Numerical examples are also presented to validate the theoretical findings.