Hyperfunction Method for Numerical Integrations

Abstract

Abstract. We examine Hirayama’s numerical integration method for integrals over finite intervals, which is called the “hyperfunction method” in this paper. In the hyperfunction method, an integral is transformed into a complex integral on a closed contour and is approximated by the trapezoidal rule,which gives good results for integrals in the case that the integrands are periodic functions. Numerical examples show that the hyperfunction method is effective for integrals with strong end-point singularities. We also remark that the relation between the hyperfunction method and the hyperfuction theory.