On the reduction of Dirichlet-Newton problems to the wing equation (Q1820042)

This paper presents a special method for solving problems with Dirichlet- Newton boundary conditions. The proposed method consists of reducing the problem to a discrete problem by means of the finite Fourier transform. This in turn is transformed to the aircraft wings singular integro- differential equation. Using the orthogonal Chebyshev polynomials, the latter equation can be reduced to an infinite system of algebraic equations. We illustrate the method by using a typical problem: the stationary heat equation within the unit circle. However, its application to initial mixed problems of the ''Dirichlet-Newton'' type may constitute the subject of a consequential paper.