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High-order finite-difference methods for Poisson’s equation


Author: H. J. van Linde
Journal: Math. Comp. 28 (1974), 369-391
MSC: Primary 65N05
DOI: https://doi.org/10.1090/S0025-5718-1974-0362936-2
MathSciNet review: 0362936
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Abstract: Finite-difference approximations to the three boundary value problems for Poisson’s equation are given with discretization errors of $O({h^3})$ for the mixed boundary value problem, $O({h^3}|\ln h|)$ for the Neumann problem and $O({h^4})$ for the Dirichlet problem, respectively. These error bounds are an improvement upon similar results obtained by Bramble and Hubbard; moreover, all resulting coefficient matrices are of positive type.


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Article copyright: © Copyright 1974 American Mathematical Society