Error diagnostics for matched asymptotic expansions
C. J. Chapman (Keele University, UK)
When an approximate solution of a physical problem is based on the assumption that a parameter is small, a natural question is how to estimate roughly the accuracy of the approximate solution when the value of the parameter is specified. Usually, other variables are present, for example a position coordinate; then at a fixed value of the parameter, the accuracy of the approximate solution depends strongly on position. This is particularly true when the exact solution contains a boundary layer. This talk concerns the construction of a simple function, called the `error diagnostic’, which when plotted as a function of position at a fixed value of the parameter gives an `error diagnostic plot’ for estimating the structure of the error.