MSC:
30E10,
30E20,
65E05,
65N12,
65N38 | MR 3010241 | Zbl 1274.30146 | DOI: 10.1007/s10492-012-0038-3

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Cauchy-type integral; Dini continuous density; piecewise linear interpolation; uniform convergence; complex variable boundary element method

References:

[1] Khubezhty, Sh. S.: **Quadrature formulas for singular integrals with Cauchy kernel**. Vladikavkaz. Mat. Zh. 10 (2008), 61-75 Russian \MR 2461693. MR 2461693

[2] II, T. V. Hromadka, Lai, C.: **The Complex Variable Boundary Element Method in Engineering Analysis**. Springler New York (1987).

[3] Whitley, R. J., II, T. V. Hromadka: **Theoretical developments in the complex variable boundary element method**. Eng. Anal. Bound. Elem. 30 (2006), 1020-1024. DOI 10.1016/j.enganabound.2006.08.002

[4] Whitley, R. J., II, T. V. Hromadka: **The existence of approximate solutions for two-dimensional potential flow problems**. Numer. Methods Partial Differ. Equations 12 (1996), 719-727. DOI 10.1002/(SICI)1098-2426(199611)12:6<719::AID-NUM5>3.0.CO;2-V | MR 1419772

[5] Lu, J. K.: **Boundary Value Problems for Analytic Functions**. World Scientific Publishing Company Singapore (1993). MR 1279172 | Zbl 0818.30027

[6] Privalov, I. I.: **The boundary properties of analytical functions**. CITTL Moscow (1950), Russian. MR 0047765

[7] Muskhelishvili, N. I.: **Singular integral equations**. Fizmatgiz Moscow (1962), Russian. MR 0355494 | Zbl 0103.07502