Dergiler / Gazi University Journal of Science / 2018 / Cilt: 31 - Sayı: 3

On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels

Sayfa
879–888
Yayın Tarihi
2022-10-19
DOI
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Yapay Zeka Hızlı Bakış & Çıkarımlar

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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The proposedmethod is very robust and capable of handling fast oscillatory integral equations.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this work we used radial kernels for computing more generalized fast oscillatory integralequations.
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Temel Bulgular & Veri:The proposed method is based on radial kernels.
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Sonuç & Katkı:The proposedmethod is very robust and capable of handling fast oscillatory integral equations.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this work we used radial kernels for computing more generalized fast oscillatory integralequations. The proposed method is based on radial kernels. The present method is efficient forcomputing oscillatory integral equations with large oscillation parameters. The proposedmethod is very robust and capable of handling fast oscillatory integral equations.

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Bu Makaleye Atıf Yap

ULLAH, Z. M., UDDIN, M., ALI, A. (2022). On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels. Gazi University Journal of Science, Cilt: 31 - Sayı: 3, 879–888. https://ajindex.com/articles/521462

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Kaynakça (11)

  1. Brunner. H., “Collocation Methods for Volterra Integral and Related Functional Equations”, Cambridge University Press, Cambridge, (2004).
  2. Davies. P. J., Duncan. D. B., “Stability and convergence of collocation schemes for retarded potential integral equations”, SIAM journal on numerical analysis, 42(3): 1167-1188, (2004).
  3. De Hoog. F., Weiss. R., “On the solution of Volterra integral equations of the first kind”, Numerische Mathematik, 21(1): 22-32, (1973).
  4. Brunner. H., Iserles. A., Norsett. S., “Open problems in the computational solution of Volterra functional equations with highly oscillatory kernels”, Isaac Newton Institute, HOP 2007, (2007).
  5. Iserles. A., Norsett. S. P, “On quadrature methods for highly oscillatory integrals and their implementation”, BIT Numerical Mathematics, 44(4): 755-772, (2004). Linz. P, “Product integration methods for Volterra integral equations of the first kind”, BIT Numerical Mathematics, 11(4): 413-421, (1971). Levin. D, “Fast integration of rapidly oscillatory functions”, Journal of Computational and Applied Mathematics, 67(1): 95-101, (1996). Levin. D, “Procedures for computing one- and two-dimensional integrals of functions with rapid irregular oscillations”, Math. Comput., 38: 531-538, (1982). Longman. I. M., “A method for numerical evaluation of finite integrals of oscillatory functions”, Mathematics of Computation, 14(69): 53-59, (1960).
  6. Polyanin.A. D., Manzhirov. A. V., “Handbook of Integral Equations”, CRC Press, (2008). Chen. R., “Numerical approximation for highly oscillatory {Bessel} transform and applications”, Journal of Mathematical Analysis and Applications, 421(2): 1635-1650, (2015).
  7. Fasshauer. G., Mc Court. M., “Kernel-based approximation methods using Matlab”, World Scientific Publishing Co Inc, (2015).
  8. Sarler. B., Vertnik. R., “Meshfree explicit local radial basis function collocation method for diffusion problems”, Computers and mathematics with applications, 51(8): 1269-1282, (2006).
  9. Uddin. M, Minullah. Z., Ali. A, “On the local kernel based approximation of highly oscillatory integrals”, Miskolc Mathematical Notes, 16(2): 1253-1264, (2015).
  10. Wang. H., Xiang. S, “Asymptotic expansion and Filon-type methods for a Volterra integral equation with a highly oscillatory kernel”, IMA Journal of Numerical Analysis, 31(2): 469-490, (2010).
  11. Piessens. R., Branders. M., “Modified Clenshaw-Curtis method for the computation of {Bessel} functions integralsl”, BIT Numerical Mathematics, 23(3): 370-381, (1983). Piessens.