On computing uniformly valid approximations for viscous waves on a plane beach
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
A high order, progressive method for the evaluation of irregular oscillatory integrals
Applied Numerical Mathematics
A method to generate generalized quadrature rule for oscillatory integrals
Applied Numerical Mathematics
Some theoretical aspects of generalised quadrature methods
Journal of Complexity
On numerical computation of integrals with integrands of the form f(x)sin(w/xr) on [0, 1]
Journal of Computational and Applied Mathematics
Suitable Gauss and Filon-type methods for oscillatory integrals with an algebraic singularity
Applied Numerical Mathematics
A short tale of long tail integration
Numerical Algorithms
Applied Numerical Mathematics
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The problem of evaluating infinite range irregularly oscillatory integrals is considered using the generalised quadrature approach based on Lagrange's identity. Some modifications are required beyond the method as applied to finite range problems and a series of practical examples are given. These split into two categories: those with exponentially decreasing weight functions and those without.