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Quadrature methods for solving Theodorsen’s singular integral equation. (English. Russian original) Zbl 1074.65152
Russ. Math. 47, No. 8, 79-82 (2003); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2003, No. 8, 82-85 (2003).
Introduction: Summary: We investigate the quadrature methods for solving Theodorsen’s singular integral equation \[ \varphi(s)+ {\lambda\over 2\pi} \int^{2\pi}_0 \ln\rho(\varphi(\sigma))\text{ctg} {\sigma- s\over 2} d\sigma= y(s),\tag{1} \] where \(\lambda\) is the numerical parameter, \(\rho(s)\) and \(y(s)\) are the known \(2\pi\)-periodic functions, and \(\varphi(s)\) is the desired function. The singular integral is understood here as the Cauchy-Lebesgue principal value. This equation is used in theory of conformal mappings and in a number of applications. Numerous results exist concerning the approximate approaches for solving equation (1).
MSC:
65R20 Numerical methods for integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
30C20 Conformal mappings of special domains
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