Approximation of oscillatory Bessel integral transforms

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Date

2023

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Elsevier

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Metallurgical and Materials Engineering
(2004)
The main fields of operation for Metallurgical and Materials Engineering are production of engineering materials, defining and improving their features, as well as developing new materials to meet the expectations at every aspect of life and the users from these aspects. Founded in 2004 and graduated its 10th-semester alumni in 2018, our Department also obtained MÜDEK accreditation in the latter year. Offering the opportunity to hold an internationally valid diploma through the accreditation in question, our Department has highly qualified and experienced Academic Staff. Many of the courses offered at our Department are supported with various practice sessions, and internship studies in summer. This way, we help our students become better-equipped engineers for their future professional lives. With the Cooperative Education curriculum that entered into effect in 2019, students may volunteer to work at contracted companies for a period of six months with no extensions to their period of study.

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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.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Description

Khan, Suliman/0000-0003-0069-4025; khan, Feroz/0000-0002-7318-4918; alhazmi, sharifah/0000-0002-7761-4196; Arshad, Muhammad/0000-0002-4283-0307; Park, Jongee/0000-0003-1415-6906

Keywords

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

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Citation

2

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Volume

208

Issue

Start Page

727

End Page

744

URI

https://doi.org/10.1016/j.matcom.2023.01.028
 https://hdl.handle.net/20.500.14411/2575

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