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On solution of a nonlocal problem with dynamic boundary conditions for a loaded linear parabolic equation by straight-line methods
Journal: Bulletin of Computational Applied Mathematics (Bull CompAMa) (Vol.5, No. 1)Publication Date: 2017-06-30
Authors : Zakir Khankishiyev;
Page : 77-98
Keywords : Nonlocal problem; loaded parabolic equation; dynamic boundary condition; straight lines method; numerical solution; maximum principle; rate of convergence;
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Abstract
We consider a nonlocal problem with dynamic boundary conditions for a loaded linear parabolic equation. For this problem we prove the unique solvability in Sobolev's spaces and the maximum principle under some natural conditions. We suggest the numerical straight-lines method for the finding of the solution of the problem. The convergence of the straight-lines method to the exact solution is also proved.
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Last modified: 2018-08-05 09:29:59