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On the propagation of round-off errors in the numerical treatment of the wave equation

Author: Arnold N. Lowan
Journal: Math. Comp. 14 (1960), 223-228
MSC: Primary 65.00
MathSciNet review: 0119431
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Abstract: An upper bound of the norm of the error vector after n time steps is $ \tfrac{1}{2}(n + 1)(n + 2)\Vert {{\delta ^{\ast}}}\Vert$. For the explicit scheme $ {\delta ^{\ast}} = \Vert {{\delta ^{\ast}}}\Vert = 3 \times \tfrac{1}{2} \times {10^{ - p}}$ where p is the number of decimals carried in the computations. For the implicit scheme $ {\delta ^{\ast}} = \Vert {{\delta ^{\ast}}}\Vert$ is an upper bound of the errors which arise both from using approximations to $ {A^{ - 1}}$ and $ {A^{ - 1}}B$ in the determination of $ {u_{k + 1}}$ from equation (6$ ^{*}$) and from rounding off the values of the products and quotients involved in the computation of the components of $ {u_{k + 1}}$.

References [Enhancements On Off] (What's this?)

  • [1] R. D. Richtmeyer, Difference Methods for Initial-Value Problems, Interscience Publishers, Inc., New York, 1957. MR 0093918 (20:438)
  • [2] A. N. Lowan, The Operator Approach to Problems of Stability and Convergence, Scripta Mathematica, Yeshiva University, New York, 1957, p. 55, p. 82-86.
  • [3] A. N. Lowan, ``On the propagation of round-off errors in the numerical integration of the heat equation,'' Math. Comp., v. 14, 1960, p. 139-146. MR 0119430 (22:10192a)

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Article copyright: © Copyright 1960 American Mathematical Society

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