Geodesic
Explicit Solution of Bitsadze-Samarskii Problem
Mathematics and Education in Mathematics, Tome 39 (2010) no. 1, pp. 114-122

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In this paper we find an explicit solution of Bitsadze-Samarskii problem for Laplace equation using operational calculus approach, based on two non-classical one-dimensional convolutions and a two-dimensional convolution. In fact, the explicit solution obtained is a way for effective summation of a solution obtained in the form of non-harmonic Fourier sine-expansion. This explicit solution is suitable for numerical calculation too. *2000 Mathematics Subject Classification: 44A35, 35L20, 35J05, 35J25.
Keywords: Nonlocal BVP, Right-Inverse Operator, Extended Duamel Principle, Generalized Solution, Non-Classical Convolution, Multiplier, Multiplier Fraction 
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Dimovski, Ivan; Tsankov, Yulian. Explicit Solution of Bitsadze-Samarskii Problem. Mathematics and Education in Mathematics, Tome 39 (2010) no. 1, pp. 114-122. http://geodesic.mathdoc.fr/item/MEM_2010_39_1_a7/