UNIDIMENSIONAL NUMERICAL SOLUTION ERROR ESTIMATION FOR CONVERGENT APPARENT ORDER

Abstract

Numerical solutions of eight differential equations in fluid dynamics are obtained by the finite-difference method with uniform unidimensional grids and with six types of numerical approximations. The main purpose of this work is to calculate uncertainties of numerical solutions using the Richardson error estimator and another estimator which is introduced in this work. These estimators are examined for reliability and accuracy of the uncertainty for the situation in which the size of the grid elements is small. In this case, as is shown in this work, two values of uncertainty can be found that bound the discretization error.