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Transfer of boundary conditions for Poisson’s equation on a circle. (English) Zbl 0797.65087

The method of transfer of boundary conditions is generalized for the case of the Dirichlet problem for the Poisson equation on a circle. The representation of the solution in the form of a Fourier series is used.

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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References:

[1] G. H. Meyer: Initial value methods for boundary value problems-Theory and applications of invariant imbedding. Academic Press, New York, 1973. · Zbl 0304.34018
[2] J. Taufer: Lösung der Randwertprobleme für Systeme von linearen Differentialgleichungen. Rozpravy ČSAV 5, 83 (1973). · Zbl 0276.34009
[3] P. Přikryl, J. Taufer, E. Vitásek: Transfer of conditions for singular boundary value problems. Apl. mat. 34 (1989), 246-258. · Zbl 0685.65078
[4] I. M. Ryzhyk, I. S. Gradshtein: Tables of integrals, sums, series and products. GITTL, Moscow, 1951.
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