U Jin Choi

Abstract In the recent works ( Commun. Numer. Meth. Engng 2001; 17 : 881; to appear), the superiority of the non‐linear transformations containing a real parameter b ≠ 0 has been demonstrated in numerical evaluation of weakly singular integrals. Based on these transformations, we define a so‐called parametric sigmoidal transformation and employ it to evaluate the Cauchy principal value and Hadamard finite‐part integrals by using the Euler–Maclaurin formula. Better approximation is expected due t

Abstract Two trigonometric quadrature formulae, one of non‐interpolatory type and one of interpolatory type for computing the hypersingular integral ${\int\hskip-0.33cm=}_{-1}^{1} w(\tau)g(\tau)/(\tau-t)^{2} \,{\rm d}\tau$ are developed on the basis of trigonometric quadrature formulae for Cauchy principal value integrals. The formulae use the cosine change of variables and trigonometric polynomial interpolation at the practical abscissae. Fast three‐term recurrence relations for evaluating the

Abstract We propose and analyze the spectral collocation approximation for the partial integro-differential equations with a weakly singular kernel. The space discretization is based on the pseudo-spectral method, which is a collocation method at the Gauss-Lobatto quadrature points. We prove unconditional stability and obtain the optimal error bounds which depend on the time step, the degree of polynomial and the Sobolev regularity of the solution.

In this letter we present a generic Craig form for the two-dimensional (2-D) Gaussian Q-function. The presented Craig form provides an alternative solution to the problems of computing probabilities involving a form of the 2-D Gaussian Q-function.

The Born iterative method(BIM) and the distorted Born iterative method (DBIM) in inverse scattering problem are analyzed. The sufficient conditions of the object function for the convergence of the BIM and the DBIM are derived.

Neuromyelitis optica spectrum disorder (NMOSD) is an autoimmune diseases of the central nervous system, and often influence optic nerve and medulla oblongata. Previous studies found out that brain abnormalities were not rare in these patients. Medulla oblongata (MO) was commonly involved and usually located at dorsal part. Patients who diagnosed NMOSD with MO lesions were more likely to have dysphagia. Previous reports indicated that the symptoms and signs of NMOSD patients could be controlled a