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  1. Computational Mathematics and Mathematical Physics
  2. Computational Mathematics and Mathematical Physics : Volume 56
  3. Computational Mathematics and Mathematical Physics : Volume 56, Issue 3, March 2016
  4. Justification of the Galerkin method for hypersingular equations
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Computational Mathematics and Mathematical Physics : Volume 57
Computational Mathematics and Mathematical Physics : Volume 56
Computational Mathematics and Mathematical Physics : Volume 56, Issue 12, December 2016
Computational Mathematics and Mathematical Physics : Volume 56, Issue 11, November 2016
Computational Mathematics and Mathematical Physics : Volume 56, Issue 10, October 2016
Computational Mathematics and Mathematical Physics : Volume 56, Issue 9, September 2016
Computational Mathematics and Mathematical Physics : Volume 56, Issue 8, August 2016
Computational Mathematics and Mathematical Physics : Volume 56, Issue 7, July 2016
Computational Mathematics and Mathematical Physics : Volume 56, Issue 6, June 2016
Computational Mathematics and Mathematical Physics : Volume 56, Issue 5, May 2016
Computational Mathematics and Mathematical Physics : Volume 56, Issue 4, April 2016
Computational Mathematics and Mathematical Physics : Volume 56, Issue 3, March 2016
On the principal and strictly particular solutions to infinite systems
On conditions for permutability of Toeplitz and Hankel matrices
Analogue of Newton–Cotes formulas for numerical integration of functions with a boundary-layer component
Reconstruction of random-disturbance amplitude in linear stochastic equations from measurements of some of the coordinates
Numerical algorithm for solving mathematical programming problems with a smooth surface as a constraint
Application of linear programming techniques for controlling linear dynamic plants in real time
On a class of optimal control problems with distributed and lumped parameters
Analysis of stability boundaries of satellite’s equilibrium attitude in a circular orbit
Justification of the Galerkin method for hypersingular equations
Long-time convergence of numerical approximations for 2D GBBM equation
Track method for the calculation of plasma heating by charged thermonuclear reaction products for axisymmetric flows
Numerical solution of the equilibrium problem for a membrane with embedded rigid inclusions
Effective solving of three-dimensional gas dynamics problems with the Runge-Kutta discontinuous Galerkin method
Unsteady rarefied gas flow in a microchannel driven by a pressure difference
Inverse problem of determining parameters of inhomogeneity of a body from acoustic field measurements
On the complexity of some quadratic Euclidean 2-clustering problems
Computational Mathematics and Mathematical Physics : Volume 56, Issue 2, February 2016
Computational Mathematics and Mathematical Physics : Volume 56, Issue 1, January 2016
Computational Mathematics and Mathematical Physics : Volume 55
Computational Mathematics and Mathematical Physics : Volume 54
Computational Mathematics and Mathematical Physics : Volume 53
Computational Mathematics and Mathematical Physics : Volume 52
Computational Mathematics and Mathematical Physics : Volume 51
Computational Mathematics and Mathematical Physics : Volume 50
Computational Mathematics and Mathematical Physics : Volume 49
Computational Mathematics and Mathematical Physics : Volume 48
Computational Mathematics and Mathematical Physics : Volume 47
Computational Mathematics and Mathematical Physics : Volume 46

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Justification of the Galerkin method for hypersingular equations

Content Provider Springer Nature Link
Author Emiv, S. I. Emiva, V. S.
Copyright Year 2016
Abstract The paper presents a theoretical study of hypersingular equations of the general form for problems of electromagnetic-wave diffraction on open surfaces of revolution. Justification of the Galerkin is given. The method is based on the separation of the principal term and its analytic inversion. The inverse of the principal operator is completely continuous. On the basis of this result, the equivalence of the initial equation to a Fredholm integral equation of the second kind is proven. An example of numerical solution with the use of Chebyshev polynomials of the second kind is considered.
Starting Page 417
Ending Page 425
Page Count 9
File Format PDF
ISSN 09655425
Journal Computational Mathematics and Mathematical Physics
Volume Number 56
Issue Number 3
e-ISSN 15556662
Language English
Publisher Pleiades Publishing
Publisher Date 2016-05-11
Publisher Place Moscow
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword hypersingular equations Galerkin method justification of the Galerkin method equations of electromagnetic-wave diffraction Computational Mathematics and Numerical Analysis
Content Type Text
Resource Type Article
Subject Computational Mathematics
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