A well-conditioned and efficient Levin method for highly oscillatory integrals with compactly supported radial basis functions

Khan S. Zaman S. Arshad M. Kang H. Shah H.H. Issakhov A.
1 October 2021 Elsevier Ltd

Engineering Analysis with Boundary Elements
2021 #131 51 - 63 pp.

Highly oscillatory integrals are frequently involved in applied problems, particularly for large-scale data and high frequencies. Levin method with global radial basis functions was implemented for numerical evaluation of these integrals in the literature. However, when the frequency is large or nodal points are increased, the Levin method with global radial basis functions faces several issues such as large condition number of the interpolation matrix and computationally inefficiency of the method, etc. In this paper, the Levin method with compactly supported radial basis functions is proposed to handle deficiencies of the method. In addition, theoretical error bounds and stability analysis of the proposed methods are performed. Several numerical examples are included to verify the accuracy, efficiency, and well-conditioned behavior of the proposed methods.

Compactly supported radial basis functions , Highly oscillatory integrals , Hybrid functions , Levin method , Stable algorithms

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School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, China
Faculty of Architecture, Allied Sciences and Humanities, University of Engineering and Technology, Peshawar, Pakistan
Department of Mathematics, Abbottabad University of Science and Technology, Pakistan
Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, Zhejiang, China
Department of Mathematical Sciences, Balochistan University of Information Technology Engineering and Management Sciences, Quetta, Pakistan
Department of Mathematical and Computer Modelling, Al-Farabi Kazakh National University Almaty Kazakhistan, Kazakh-British Technical University, Almaty, Kazakhstan
Deparment of Mathematics and Cybernetics, Kazakh British Technical University, 050000, Almaty, Almaty, Kazakhstan

School of Mathematics and Statistics
Faculty of Architecture
Department of Mathematics
Department of Mathematics
Department of Mathematical Sciences
Department of Mathematical and Computer Modelling
Deparment of Mathematics and Cybernetics

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