Research Article

On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels

Volume: 31 Number: 3 September 1, 2018
  • Amjad Alı
  • Zeyad Min Ullah
  • Marjan Uddın
EN

On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels

Abstract

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

Keywords

References

  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).
  6. Linz. P, “Product integration methods for Volterra integral equations of the first kind”, BIT Numerical Mathematics, 11(4): 413-421, (1971).
  7. Levin. D, “Fast integration of rapidly oscillatory functions”, Journal of Computational and Applied Mathematics, 67(1): 95-101, (1996).
  8. Levin. D, “Procedures for computing one- and two-dimensional integrals of functions with rapid irregular oscillations”, Math. Comput., 38: 531-538, (1982).

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Amjad Alı This is me
Türkiye

Zeyad Min Ullah This is me

Marjan Uddın This is me

Publication Date

September 1, 2018

Submission Date

August 28, 2018

Acceptance Date

August 28, 2018

Published in Issue

Year 2018 Volume: 31 Number: 3

APA
Alı, A., Ullah, Z. M., & Uddın, M. (2018). On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels. Gazi University Journal of Science, 31(3), 879-888. https://izlik.org/JA98UK72SK
AMA
1.Alı A, Ullah ZM, Uddın M. On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels. Gazi University Journal of Science. 2018;31(3):879-888. https://izlik.org/JA98UK72SK
Chicago
Alı, Amjad, Zeyad Min Ullah, and Marjan Uddın. 2018. “On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels”. Gazi University Journal of Science 31 (3): 879-88. https://izlik.org/JA98UK72SK.
EndNote
Alı A, Ullah ZM, Uddın M (September 1, 2018) On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels. Gazi University Journal of Science 31 3 879–888.
IEEE
[1]A. Alı, Z. M. Ullah, and M. Uddın, “On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels”, Gazi University Journal of Science, vol. 31, no. 3, pp. 879–888, Sept. 2018, [Online]. Available: https://izlik.org/JA98UK72SK
ISNAD
Alı, Amjad - Ullah, Zeyad Min - Uddın, Marjan. “On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels”. Gazi University Journal of Science 31/3 (September 1, 2018): 879-888. https://izlik.org/JA98UK72SK.
JAMA
1.Alı A, Ullah ZM, Uddın M. On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels. Gazi University Journal of Science. 2018;31:879–888.
MLA
Alı, Amjad, et al. “On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels”. Gazi University Journal of Science, vol. 31, no. 3, Sept. 2018, pp. 879-88, https://izlik.org/JA98UK72SK.
Vancouver
1.Amjad Alı, Zeyad Min Ullah, Marjan Uddın. On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels. Gazi University Journal of Science [Internet]. 2018 Sep. 1;31(3):879-88. Available from: https://izlik.org/JA98UK72SK