Approximation of oscillatory Bessel integral transforms

Suliman Khan, Sakhi Zaman, Muhammad Arshad, Sharifah E. Alhazmi, Feroz Khan and Jongee Park

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 208, issue C, 727-744

Abstract: The numerical treatment of oscillatory integrals is a demanding problem in applied sciences, particularly for large-scale problems. The main concern of this work is on the approximation of oscillatory integrals having Bessel-type kernels with high frequency and large interpolation points. For this purpose, a modified meshless method with compactly supported radial basis functions is implemented in the Levin formulation. The method associates a sparse system matrix even for high frequency values and large data points, and approximates the integrals accurately. The method is efficient and stable than its counterpart methods. Error bounds are derived theoretically and verified with several numerical experiments.

Keywords: Highly oscillatory Bessel integral transforms; Compactly supported radial basis functions; Stable algorithms; Levin method; Hybrid functions (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:208:y:2023:i:c:p:727-744

DOI: 10.1016/j.matcom.2023.01.028

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