Approximation of oscillatory Bessel integral transforms

Khan, Suliman
Zaman, Sakhi
Arshad, Muhammad
Alhzami, Sharifah E.
Khan, Feroz
Park, Jongee
Journal Title
Journal ISSN
Volume Title
Mathematics and Computers in Simulation
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.
Published by Mathematics and Computers in Simulation;; Suliman Khan, Interdisciplinary Research Center for Intelligent Manufacturing and Robotics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia; Sakhi Zaman, Faculty of Architecture, Allied Sciences and Humanities, University of Engineering and Technology, Peshawar, Pakistan; Muhammad Arshad, Department of Mathematics, Abbottabad University of Science and Technology, Pakistan; Sharifah E. Alhazmi, Mathematics Department, Al-Qunfudah University College, Umm Al-Qura University, Mecca 2438, Saudi Arabia; Feroz Khan,Hitec University, Taxila, Punjab, Pakistan; Jongee Park, Department of Metallurgical and Materials Engineering, Atilim University, Ankara 06836, Turkey.
Highly oscillatory Bessel integral transforms; Compactly supported radial basis functions Stable algorithms; Levin method; Hybrid functions