Filon–Clenshaw–Curtis formulas for highly oscillatory integrals in the presence of stationary points

2017 ◽  
Vol 117 ◽  
pp. 87-102 ◽  
Author(s):  
Hassan Majidian
Keyword(s):  
Oscillatory Integrals ◽  
Stationary Points ◽  
Highly Oscillatory ◽  
Highly Oscillatory Integrals

scholarly journals Moment-free numerical approximation of highly oscillatory integrals with stationary points

2007 ◽  
Vol 18 (4) ◽  
pp. 435-447 ◽  
Author(s):  
SHEEHAN OLVER
Keyword(s):  
Asymptotic Expansion ◽  
Stationary Phase ◽  
Asymptotic Behaviour ◽  
Approximation Method ◽  
Numerical Approximation ◽  
Oscillatory Integrals ◽  
Numerical Quadrature ◽  
Stationary Points ◽  
Highly Oscillatory ◽  
Highly Oscillatory Integrals

This article presents a method for the numerical quadrature of highly oscillatory integrals with stationary points. We begin with the derivation of a new asymptotic expansion, which has the property that the accuracy improves as the frequency of oscillations increases. This asymptotic expansion is closely related to the method of stationary phase, but presented in a way that allows the derivation of an alternate approximation method that has similar asymptotic behaviour, but with significantly greater accuracy. This approximation method does not require moments.

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