On Computation of Bessel and Airy Oscillatory Integral Transforms

ABSTRACT In applied sciences, the analysis of Bessel and Airy oscillatory integrals is a demanding problem, particularly for large‐scale data points and large frequency parameters. The Levin method, with global radial basis functions, is an accurate tool for approximating these integrals. But as the interpolation points or frequency increase, the interpolation matrix becomes dense and highly ill‐conditioned. To ensure a stable and efficient computation of Bessel and Airy integrals, we implement the Levin method with compactly supported radial basis functions. Although the accuracy of the new algorithm has not significantly improved compared to the counterpart methods. Alternatively, the method exhibits faster and well‐conditioned behavior, even for large numbers of data points and large frequency parameters. The convergence analysis of the method is performed and numerically verified with several benchmark problems.