2019/09/11 by Ogata, Hidenori
#65D30 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1909.04911
In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is defined by an integral of the Fourier-Laplace transform type, and we obtain the desired integral by the analytic continuation of this analytic function onto the real axis using a continued fraction. We also remark that the proposed method is related to hyperfunction theory, a theory of generalized functions based on complex function theory. Numerical examples show the effectiveness of the proposed method.