Recovery of the intermediate derivative of an approximately given function

Abstract

The problem of numerical recovery of intermediate derivatives or a differential operator is considered. With this aim, the norm of the leading derivative is estimated, from which optimal difference schemes for intermediate derivatives are obtained. An example of a smooth model function is considered for which the measurement error is simulated using real-world experimental data. The trusted probability of the obtained estimate for the norm of the leading derivative is estimated. Intervals of trusted recovery of intermediate derivatives are estimated