Abstract
An estimate O(τ + h 2)ln(j + 1) of the convergence rate for the solution of a four-point implicit difference scheme used for approximations on a uniform grid of a one-dimensional heat equation is obtained, with the provision that the boundary and initial data are subject at corner points only to the continuity condition, with no other compatibility conditions being satisfied. A discrete Green’s function is used to obtain an a priori estimate of the grid solution in terms of the appropriate negative norm of the right-hand side.
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More From: Moscow University Computational Mathematics and Cybernetics
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