Numerical approximations to integrals with a highly oscillatory Bessel kernel

2012 ◽  
Vol 62 (5) ◽  
pp. 636-648 ◽  
Author(s):  
Ruyun Chen
Keyword(s):  
Numerical Approximations ◽  
Highly Oscillatory ◽  
Bessel Kernel

scholarly journals On Computation of Highly Oscillatory Integrals with Bessel Kernel

2019 ◽  
pp. 51-63
Author(s):  
Muhammad Munib Khan ◽  
Sakhi Zaman
Keyword(s):  
Special Form ◽  
Numerical Scheme ◽  
Oscillatory Integrals ◽  
Numerical Examples ◽  
Highly Oscillatory ◽  
Bessel Kernel ◽  
Highly Oscillatory Integrals ◽  
The Given ◽  
Fourier Kernel

In this paper, we introduce a new numerical scheme for approximation of highly oscillatory integrals having Bessel kernel. We transform the given integral to a special form having improper nonoscillatory Laguerre type and proper oscillatory integrals with Fourier kernels. Integrals with Laguerre weights over [0, ∞) will be solved by Gauss-Laguerre quadrature and oscillatory integrals with Fourier kernel can be evaluated by meshless-Levin method. Some numerical examples are also discussed to check the efficiency of proposed method.

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