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Volume 14, Issue 3
A High-Order Piecewise Quartic Spline Rule for Hadamard Integral and Its Application of the Cavity Scattering

Meiling Zhao, Wenjie He & Gendai Gu

Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 811-838.

Published online: 2021-06

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  • Abstract

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.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ggd999@126.com (Gendai Gu)

  • BibTex
  • RIS
  • TXT
@Article{NMTMA-14-811, author = {Zhao , MeilingHe , Wenjie 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 = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2020-0163 }, url = {http://global-sci.org/intro/article_detail/nmtma/19199.html} }
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 -

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.

Meiling Zhao, Wenjie He & Gendai Gu. (2021). A High-Order Piecewise Quartic Spline Rule for Hadamard Integral and Its Application of the Cavity Scattering. Numerical Mathematics: Theory, Methods and Applications. 14 (3). 811-838. doi:10.4208/nmtma.2020-0163
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