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Journals / International Journal of Informatics and Applied Mathematics / 2019 / Volume: 2 Issue: 2

Numerical Approximation of Highly Oscillatory Integrals with Weak Singularity

İrfan Ullah(Department of Basic Sciences, University of Engineering and Technology Peshawar, Peshawar, Pakistan)
Muhammad Munib Khan(University of Engineering and Technology peshawar, pakistan)
Pages
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Publication Date
2019-12-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

To check the effectiveness of method results of some test problems are calculated by hybrid function quadrature and compared with the results produces by the proposed method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we design an accurate scheme for the approximation of highly oscillatory integrals having singularity .
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Key Findings & Data:The interval of integration [a,b] is divided into two subintervals and then approximate the integral over first interval by hybrid function quadrature (Q_hf [g]), while for the approximation of integrals over the second interval we use Levin meshless method (Q_L^m [g]).
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Conclusion & Impact:To check the effectiveness of method results of some test problems are calculated by hybrid function quadrature and compared with the results produces by the proposed method.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:oscillatort integral · singularity · Levin method

Abstract

In this paper, we design an accurate scheme for the approximation of highly oscillatory integrals having singularity . The interval of integration [a,b] is divided into two subintervals and then approximate the integral over first interval by hybrid function quadrature (Q_hf [g]), while for the approximation of integrals over the second interval we use Levin meshless method (Q_L^m [g]). For a result, we find the sum of both the integrals. To check the effectiveness of method results of some test problems are calculated by hybrid function quadrature and compared with the results produces by the proposed method.

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Cite This Article

Ullah, İ., Khan, M. M. (2019). Numerical Approximation of Highly Oscillatory Integrals with Weak Singularity. International Journal of Informatics and Applied Mathematics, Volume: 2 Issue: 2. https://ajindex.com/articles/1588943

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