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Projective methods for solving Theodorsen singular integral equation. (English. Russian original) Zbl 1161.45307
Russ. Math. 46, No. 9, 64-67 (2002); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2002, No. 9, 67-70 (2002).
The singular integral equation \[ \phi(s)+\frac\lambda{2\pi}\int\limits_0^{2\pi} \ln\rho(\phi(\sigma))\text{ctg}\frac{\sigma-s}2d\sigma=y(s), \] where the functions \(\rho\) and \(y\) are given, is studied in this paper.
Existence and uniqueness theorems for the solution are given. Using the theory of monotone operators, the author formulates approximation theorems.
No proofs are given.
45G05 Singular nonlinear integral equations
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
45E05 Integral equations with kernels of Cauchy type
45L05 Theoretical approximation of solutions to integral equations
65R20 Numerical methods for integral equations