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- Pawel Karczmarek, Dorota Pylak, Michail A. Sheshko
- Applied Mathematics and Computation
- 2006

where D = (−1, 1)× (−1, 1) , f(x, y) is a given Hölder continuous function in D, and φ(x, y) is an unknown function. The equation (1) has applications in the theory of aeroelasticity [1]. Note that the equation without logarithmic singularities was many times considered in different classes of functions. In the literature the solutions of the equation (1)… (More)

- Michail A. Sheshko, Pawel Karczmarek, Dorota Pylak, Pawel Wójcik
- Computers & Mathematics with Applications
- 2014

- Dorota Pylak, Pawel Karczmarek, Michail A. Sheshko
- Applied Mathematics and Computation
- 2010

In this paper, exact solutions of the characteristic and dominant equation with Cauchy kernel on the real line are presented. Next, trigonometric polynomials are used to derive approximate solutions of these equations. Moreover, estimations of errors of the approximated solutions are presented and proved. 2010 Elsevier Inc. All rights reserved.

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