||Error Criteria in Water Surface Profile Computations.
McBea, Edward A. ;
Perkin, Frank E. ;
||Massachusetts Inst. of Tech., Cambridge. Hydrodynamics Lab.
||Rept. no. ;124 ;R70-28; DI-14-01-0001-1988; MIT-DSR-71230 ;MIT-DSR-71934; 02201,; C-1495(1988)(3)
( Stream flow ;
Data processing) ;
( Computer programming ;
Numerical analysis) ;
Error analysis ;
Mathematical models ;
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Numerical error generation properties and the effects of data uncertainty are analyzed for several of the most common methods used in water surface profile computations. Theoretical equations are developed that serve as bounds on the actual errors that are introduced during the computation. The analysis also provides criteria which may be used in the rational selection of the calculation increment. In most engineering applications the effect of numerical errors on the computed profile will be considerably smaller than that due to data uncertainty. When numerical error generation is significant, it is predictable through the error bound equations. The successive substitutions algorithm, presently used in most computer programs for convergence of the iteration scheme, sometimes encounters difficulties due to convergence to incorrect profiles and failure to converge; application of the bisection algorithm eliminates these problems. (Author)