Approximation of oscillatory Bessel integral transforms

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Pages (from-to)727-744
Number of pages18
JournalMathematics and Computers in Simulation
Volume208
DOIs
StatePublished - Jun 2023

Bibliographical note

Publisher Copyright:
© 2023 International Association for Mathematics and Computers in Simulation (IMACS)

Keywords

  • Compactly supported radial basis functions
  • Highly oscillatory Bessel integral transforms
  • Hybrid functions
  • Levin method
  • Stable algorithms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

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