Integration technique for evaluating confluent hypergeometric functions and its application to functionally graded materials

Abstract

A novel numerical integral technique is proposed for evaluating confluent hypergeometric functions (CHFs), which arise from a wave propagation problem in functionally graded material (FGM). In the present method, a part of the integrand in the integral representation of the CHFs is approximated by piecewise polynomials, so that the integral can be carried out analytically in each sub-region. Using this method, the singularity of the integrand can also be dealt with easily. An error-controlled algorithm is also proposed to control the integral to a desired accuracy. The present technique is validated with existing FORTRAN routines and the MATLAB package. Furthermore, the application of this technique is presented to calculate waves propagating in FGM plate.