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A difference method for the solution of a class of generalized boundary-value problems in a half-strip

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A class of problems in a generalized formulation is studied for the case of a half-strip. A theorem is proven on the existence and uniqueness of the solution in a weighted Sobolev space; a difference scheme is constructed on a finite lattice and the rate of its convergence is established.

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Literature cited

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Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 28–37, 1989.

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Gavrilyuk, I.P., Makarov, L.V. A difference method for the solution of a class of generalized boundary-value problems in a half-strip. J Math Sci 67, 3052–3058 (1993). https://doi.org/10.1007/BF01098139

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  • Sobolev Space
  • Difference Scheme
  • Difference Method
  • Weighted Sobolev Space
  • Finite Lattice