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• W2131005749 abstract "It is well-known that non-periodic boundary conditions reduce considerably the overall accuracy of an approximating scheme. In previous papers the present authors have studied a fourth-order compact scheme for the one-dimensional biharmonic equation. It relies on Hermitian interpolation, using functional values and Hermitian derivatives on a three-point stencil. However, the fourth-order accuracy is reduced to a mere first-order near the boundary. In turn this leads to an “almost third-order” accuracy of the approximate solution. By a careful inspection of the matrix elements of the discrete operator, it is shown that the boundary does not affect the approximation, and a full (“optimal”) fourth-order convergence is attained. A number of numerical examples corroborate this effect." @default.
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• W2131005749 date "2012-06-09" @default.
• W2131005749 modified "2023-10-17" @default.
• W2131005749 title "Recent Advances in the Study of a Fourth-Order Compact Scheme for the One-Dimensional Biharmonic Equation" @default.
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• W2131005749 doi "https://doi.org/10.1007/s10915-012-9611-x" @default.
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