On the propagation of round-off errors in the numerical treatment of the wave equation
HTML articles powered by AMS MathViewer
- by Arnold N. Lowan PDF
- Math. Comp. 14 (1960), 223-228 Request permission
Abstract:
An upper bound of the norm of the error vector after n time steps is $\tfrac {1}{2}(n + 1)(n + 2)\| {{\delta ^{\ast }}}\|$. For the explicit scheme ${\delta ^{\ast }} = \| {{\delta ^{\ast }}}\| = 3 \times \tfrac {1}{2} \times {10^{ - p}}$ where p is the number of decimals carried in the computations. For the implicit scheme ${\delta ^{\ast }} = \| {{\delta ^{\ast }}}\|$ 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
- Robert D. Richtmyer, Difference methods for initial-value problems, Interscience Tracts in Pure and Applied Mathematics, Tract 4, Interscience Publishers, Inc., New York, 1957. MR 0093918 A. N. Lowan, The Operator Approach to Problems of Stability and Convergence, Scripta Mathematica, Yeshiva University, New York, 1957, p. 55, p. 82-86.
- Arnold N. Lowan, On the propagation of round-off errors in the numerical integration of the heat equation, Math. Comp. 14 (1960), 139–146. MR 119430, DOI 10.1090/S0025-5718-1960-0119430-3
Additional Information
- © Copyright 1960 American Mathematical Society
- Journal: Math. Comp. 14 (1960), 223-228
- MSC: Primary 65.00
- DOI: https://doi.org/10.1090/S0025-5718-1960-0119431-5
- MathSciNet review: 0119431