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

van Linde, H. J.

doi:10.1090/S0025-5718-1974-0362936-2

High-order finite-difference methods for Poisson’s equation
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by H. J. van Linde PDF

Math. Comp. 28 (1974), 369-391 Request permission

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.

References

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High-Order Finite Difference Methods for Poisson’s Equation

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Notices Amer. Math. Soc.