Numerical Integration Method for Oscillatory Functions over Half Infinite Interval by Partition Integration Method

Abstract

Arithmetic operations and functions of Taylor series can be defined easily by FORTRAN 90 and C++program language. Using this, it is shown that asymptotic expansion of the integral for oscillatory functions over infinite interval: ∫^∞_0f(x)g(x)dx, where f(x) is slowly decaying function, g(x) is sin x, cosx or J_n(x)(the first kind Bessel function of integer order), can be computed easily by partition integration method. Evaluating this expansion gives an effective numerical integration method for this kind of integrals.