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- W2022195477 abstract "The method of upper-lower solutions for continuous parabolic equations is extended to some finite difference system for numerical solutions. The idea of this method is that by using the upper or lower solution as the initial iteration one can obtain a monotone sequence that converges to a unique solution of the problem. The aim of this paper is to present two iterative schemes for the construction of the monotone sequence and to show that both schemes are numerically stable. These two schemes are modified Jacobi method and Gauss–Seidel method for nonlinear algebraic equations. An advantage of this approach is that each of the two methods yields an error estimate between the true solution and the computed mth iteration. On the other hand, the standard Picard type of iterative scheme is used to show that the finite difference system converges to the continuous parabolic equations." @default.
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- W2022195477 date "1987-02-01" @default.
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- W2022195477 title "Numerical Methods for Semilinear Parabolic Equations" @default.
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- W2022195477 doi "https://doi.org/10.1137/0724003" @default.
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