@Article{NMTMA-14-3,
author = {Zhao, Meiling and Wenjie, He and Gu, Gendai},
title = {A High-Order Piecewise Quartic Spline Rule for Hadamard Integral and Its Application of the Cavity Scattering},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2021},
volume = {14},
number = {3},
pages = {811--838},
abstract = {<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>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2020-0163},
url = {https://global-sci.com/article/90321/a-high-order-piecewise-quartic-spline-rule-for-hadamard-integral-and-its-application-of-the-cavity-scattering}
}