Research output: Contribution to journal › Article › peer-review
Approximate methods for solving linear and nonlinear hypersingular integral equations. / Boykov, Ilya; Roudnev, Vladimir; Boykova, Alla.
In: Axioms, Vol. 9, No. 3, 74, 01.09.2020.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Approximate methods for solving linear and nonlinear hypersingular integral equations
AU - Boykov, Ilya
AU - Roudnev, Vladimir
AU - Boykova, Alla
N1 - Publisher Copyright: © 2020 by the authors.
PY - 2020/9/1
Y1 - 2020/9/1
N2 - We propose an iterative projection method for solving linear and nonlinear hypersingular integral equations with non-Riemann integrable functions on the right-hand sides. We investigate hypersingular integral equations with second order singularities. Today, hypersingular integral equations of this type are widely used in physics and technology. The convergence of the proposed method is based on the Lyapunov stability theory of solutions of ordinary differential equation systems. The advantage of the method for linear equations is in simplicity of unique solvability verification for the approximate equations system in terms of the operator logarithmic norm. This makes it possible to estimate the norm of the inverse matrix for an approximating system. The advantage of the method for nonlinear equations is that neither the existence or reversibility of the nonlinear operator derivative is required. Examples are given illustrating the effectiveness of the proposed method.
AB - We propose an iterative projection method for solving linear and nonlinear hypersingular integral equations with non-Riemann integrable functions on the right-hand sides. We investigate hypersingular integral equations with second order singularities. Today, hypersingular integral equations of this type are widely used in physics and technology. The convergence of the proposed method is based on the Lyapunov stability theory of solutions of ordinary differential equation systems. The advantage of the method for linear equations is in simplicity of unique solvability verification for the approximate equations system in terms of the operator logarithmic norm. This makes it possible to estimate the norm of the inverse matrix for an approximating system. The advantage of the method for nonlinear equations is that neither the existence or reversibility of the nonlinear operator derivative is required. Examples are given illustrating the effectiveness of the proposed method.
KW - Hypersingular integral equations
KW - Iterative projection method
KW - Lyapunov stability theory
UR - http://www.scopus.com/inward/record.url?scp=85088385672&partnerID=8YFLogxK
U2 - 10.3390/AXIOMS9030074
DO - 10.3390/AXIOMS9030074
M3 - Article
AN - SCOPUS:85088385672
VL - 9
JO - Axioms
JF - Axioms
SN - 2075-1680
IS - 3
M1 - 74
ER -
ID: 88225162