| Abstract: | We develop a fourth-order piecewise quartic spline rule for Hadamardintegral. The quadrature formula of Hadamard integral is obtained by replacingthe integrand function with the piecewise quartic spline interpolation function. Weestablish corresponding error estimates and analyze the numerical stability. Therule can achieve fourth-order convergence at any point in the interval, even whenthe singular point coincides with the grid point. Since the derivative information ofthe integrand is not required, the rule can be easily applied to solve many practicalproblems. Finally, the quadrature formula is applied to solve the electromagneticscattering from cavities with different wave numbers, which improves the wholeaccuracy of the solution. Numerical experiments are presented to show the efficiencyand accuracy of the theoretical analysis. |
