SOLVING OF ONE-DIMENSIONAL HYPERSINGULAR INTEGRAL EQUATION USING HAAR’S WAVELETS

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

We constructed a numerical method for the one-dimensional hypersingular integral equation which uses sparse matrix approximations. This method has the same convergence order as conventional methods for hypersingular integral equations but the new method is more effective in both memory and arithmetic operations.

About the authors

D. A. Kogtenev

Marchuk Institute of Numerical Mathematics of RAS

Email: kogtenev.da@phystech.edu
Moscow, Russia

N. L. Zamarashkin

Marchuk Institute of Numerical Mathematics of RAS

Author for correspondence.
Email: nikolai.zamarashkin@gmail.com
Moscow, Russia

References

  1. Gakhov, F.D., Boundary Value Problems, Oxford: Pergamon Press, 1966.
  2. Setukha, A.V., Chislennyi metody v integral’nykh uravneniakh ee ikh prilozhenia (Numerical Methods for Integral Equations and their Applications), Moscow: Argamak-Media, 2014.
  3. Zakharov, E.V., Ryzhakov, G.V., and Setukha, A.V., Numerical solution of 3D problems of electromagnetic wave difraction on a system of ideally conducting surfaces by the method of hypersingular integral equations, Differ. Equat., 2014, vol. 55, no. 9, pp. 1240–1251.
  4. Beylkin, G., Koifman, R., and Rokhlin, V., Fast wavelet transforms and numerical algorithms, I, Comm. Pure Appl. Math., 2019, vol. 44, pp. 141–183.
  5. Chen, Z., Micchelli, C.A., and Xu, Y., Multiscale Methods for Fredholm Integral Equations, Cambridge: Cambridge University Press, 2015.
  6. Aparinov, A.A., Setukha, A.V., and Stavtsev, S.L., Low rank methods of approximation in an electromagnetic problem, Lobachevskii J. Math., 2019, vol. 40, no. 11, pp. 1771–1780.
  7. Amaratunga, K. and Castrillon-Candas, J.E., Surface wavelets: a multiresolution signal processing tool for 3D computational modelling, Int. J. Numer. Meth. Engng., 2001, vol. 55, no. 3, pp. 239–271.
  8. Saad, Y. and Schultz, M.H., GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 1986, vol. 7, no. 3, pp. 856–869.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2024 Russian Academy of Sciences