On the Rate of Convergence of Projection-Difference Methods for Smoothly Solvable Parabolic Equations |
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Authors: | V V Smagin |
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Institution: | (1) Voronezh State University, Voronezh, Russia |
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Abstract: | A linear parabolic problem in a separable Hilbert space is solved approximately by the projection-difference method. The problem is discretized in space by the Galerkin method orientated towards finite-dimensional subspaces of finite-element type and in time by using the implicit Euler method and the modified Crank-Nicolson scheme. We establish uniform (with respect to the time grid) and mean-square (in space) error estimates for the approximate solutions. These estimates characterize the rate of convergence of errors to zero with respect to both the time and space variables. |
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Keywords: | linear parabolic problem projection-difference method Galerkin method implicit Euler method Crank-Nicolson scheme separable Hilbert space |
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