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- W2029604559 abstract "The two-dimensional biharmonic operator is approximated by a finite-difference operator over a square (h × h) net, which connects each node with 16 neighbouring nodes in such a manner that the resulting matrix has “Young's Property A,” for simple boundary conditions. It is shown that the local truncation error, the convergence rate of S.O.R. for solving the finite-difference (or “net”) equations, and the truncation error of the solution of the net equations are each of order O(h2) as h → 0. Comparisons are made with the conventional 13-node approximation to the biharmonic operator: in particular, numerical experiments indicate that the convergence rate of S.O.R. for solving net equations based on the conventional 13-node operator is considerably less than that for the novel 17-node operator." @default.
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- W2029604559 date "1963-08-01" @default.
- W2029604559 modified "2023-10-18" @default.
- W2029604559 title "A Novel Finite-Difference Approximation to the Biharmonic Operator" @default.
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