A fast collocation method for acoustic scattering in shallow oceans

In this paper, we investigate the numerical solution of the integral equation of the second kind reduced by acoustic scattering in shallow oceans with Dirichlet condition. Based on analyzing the singularity of the truncating kernel with a sum of infinite series, using our trigonometric interpolatory wavelets and collocation method, we obtain the numerical solution which possesses a fast convergence rate like o(2−j). Moreover, the entries of the stiffness matrix can be obtained by FFT, which lead the computational complexity to decrease obviously.