An integration technique for evaluating confluent hypergeometric functions and its application to functionally graded materials
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.
confluent hypergeometric function functionally graded material adaptive integration function approximation elastic wave