TY - JOUR
T1 - A High-Order Piecewise Quartic Spline Rule for Hadamard Integral and Its Application of the Cavity Scattering
AU - Zhao , Meiling
AU - He , Wenjie
AU - Gu , Gendai
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 811
EP - 838
PY - 2021
DA - 2021/06
SN - 14
DO - http://doi.org/10.4208/nmtma.2020-0163 
UR - https://global-sci.org/intro/article_detail/nmtma/19199.html
KW - Hadamard integral, piecewise quartic spline rule, error estimate, electromagnetic
scattering.
AB - <p style="text-align: justify;">We develop a fourth-order piecewise quartic spline rule for Hadamard
integral. The quadrature formula of Hadamard integral is obtained by replacing
the integrand function with the piecewise quartic spline interpolation function. We
establish corresponding error estimates and analyze the numerical stability. The
rule can achieve fourth-order convergence at any point in the interval, even when
the singular point coincides with the grid point. Since the derivative information of
the integrand is not required, the rule can be easily applied to solve many practical
problems. Finally, the quadrature formula is applied to solve the electromagnetic
scattering from cavities with different wave numbers, which improves the whole
accuracy of the solution. Numerical experiments are presented to show the efficiency
and accuracy of the theoretical analysis.</p>