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Semi-discrete Time-Dependent Fourth-Order Problems on an Interval: Error Estimate

  • Dalia FishelovEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 103)

Abstract

We present high-order compact schemes for fourth-order time-dependent problems, which are related to the “buckling plate” or the “clamping plate” problems. Given a mesh size h, we show that the truncation error is O(h 4) at interior points and O(h) at near-boundary points. In addition, the convergence of these schemes is analyzed. Although the truncation error is only of first-order at near-boundary points, we have proved that the error of these schemes converges to zero as h tends to zero at least as O(h 3. 5). Numerical results are performed and they calibrate the high-order accuracy of the schemes. It is shown that the numerical rate of convergence is actually four, thus the error tends to zero as O(h 4).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Afeka-Tel-Aviv Academic College for EngineeringTel-AvivIsrael

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