Abstract
We find the exact order of the ε-complexity of weakly singular integral equations with periodic and analytic coefficients of logarithmic singularities. This class of equations includes boundary equations for outer boundary-value problems for the two-dimensional Helmholtz equation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. Wozniakowski, “Information-based complexity,”Ann. Rev. Comput. Sci., 318–380 (1986).
S. V. Pereverzev, “On the complexity of the problem of finding solutions of Fredholm equations of the second kind with smooth kernels,”Ukr. Mat. Zh.,41, No. 2, 189–193 (1989).
S. V. Pereverzev, “Hyperbolic cross and the complexity of the approximate solution of Fredholm integral equations of the second kind with differentiable kernels,”Sib. Mat. Zh.,32. No. 1, 107–115 (1991).
K. Frank, S. Heinrich, and S. V. Pereverzev,Information Complexity of Multivariate Fredholm Integral Equations in Sobolev Classes, Technical Report 263/95, University of Kaiserslautern, Kaiserslautern (1995).
S. V. Pereverzev and C. C. Shapirov, “Information complexity of the Fredholm equations of the second kind with compact operators in Hilbert space,”J. Complexity,8, No. 2, 176–202 (1992).
K. Sh. Makhkamov, “On the complexity of the problem of solution of singular integral equations,”Dokl. Akad. Nauk Ukr., No. 1, 28–34(1994).
A. Yan, “A fast numerical solution for a second kind boundary integral equation with a logarithmic kernel,”SI AM J. Numer. Anal.,31, No. 2, 477–498 (1994).
V. M. Tikhomirov,Some Problems in the Theory of Approximation [in Russian], Moscow University, Moscow 1976.
J. Saranen and G. Vainikko, “Trigonometric collocation methods with product integration for boundary integral equations on closed curves,”SIAMJ. Numer. Anal.,32, No. 2, 169–175 (1995).
L. V. Kantorovich and G. P. Akilov,Functional Analysis [in Russian], Nauka, Moscow 1977.
Rights and permissions
About this article
Cite this article
Azizov, M. On the complexity of boundary integral equations with analytic coefficients with logarithmic singularities. Ukr Math J 48, 1473–1485 (1996). https://doi.org/10.1007/BF02377816
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02377816