Significance arithmetic: Application to a partial differential equation

Abstract

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.