کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4628357 | 1631826 | 2014 | 12 صفحه PDF | دانلود رایگان |
In this paper we consider the implementation of the asymptotic Filon-type method for the semi-infinite highly oscillatory Bessel integrals of the form ∫1∞f(x)Cv(ωx)dx, where Cv(ωx)Cv(ωx) denotes Bessel function Jv(ωx)Jv(ωx) of the first kind, Yv(ωx)Yv(ωx) of the second kind, Hv(1)(ωx) and Hv(2)(ωx) of the third kind, and modified Bessel function Kv(ωx)Kv(ωx) of the second kind, respectively, f is a smooth function on [1,∞)[1,∞), limx→∞f(k)(x)=0(k=0,1,2,…) and ωω is large. By approximating f by a linear combination of negative integer powers so that the moments can be expressed by some special functions, we complete the implementation of the method. Furthermore, we give the error analysis of the method for computing the integrals. The method is very efficient in obtaining very high precision approximations if ωω is sufficiently large. Numerical examples are provided to confirm our analysis.
Journal: Applied Mathematics and Computation - Volume 228, 1 February 2014, Pages 477–488