Optimal steps in space and time for 1D advection equation with upwind difference scheme
The optimal steps in space and time are studied in numerical solution of one-dimensional advection equation with upwind difference scheme when round off error is taken into account.Firstly,discretization error and round off errors in the nu-merical computation are analyzed theoretically,as well as the accumulation of the two kinds of errors propagating from each lower time layer to the highest time layer.The theoretical approximate formula for total error bound is derived.Then the theoreti-cal formulae for determining optimal steps in space and time are obtained,and a universal relation between two optimal time steps under any two different machine precision is established,which only relates to the two involved machine precision.Final-ly,the reliability of the conclusion are confirmed by numerical examples.
advection equationupwind difference schemediscretization errorround off erroroptimal step
万方数据
维普
