Issue No.07 - July (1977 vol.26)
R.L. Bivins , Los Alamos Scientific Laboratory, University of California
The methods of significance arithmetic are applied to the numerical solution of a nonlinear partial-differential equation. Our approach permits the use of initial values having imprecision considerably greater than that of rounding error; moreover, the intermediate and final quantities are monitored so that at any stage the precision of such quantities is available. An algorithm is found that represents faithfully the solution to a difference-equation approximation to Burgers' equation.
Error analysis, sensitivity analysis.
R.L. Bivins, N.C. Metropolis, "Significance Arithmetic: Application to a Partial Differential Equation", IEEE Transactions on Computers, vol.26, no. 7, pp. 639-642, July 1977, doi:10.1109/TC.1977.1674896