| Abstrakt: |
Numerical differentiation of functions with large gradients is investigated. It is assumed that such a function contains a component known up to a factor and responsible for the large gradients of the function. Application of classical formulas for calculating derivatives to such functions may lead to significant errors. For the numerical differentiation on a uniform grid, special-purpose formulas which are exact for the boundary layer component are studied. Conditions are formulated under which an error estimate of a difference formula for a derivative does not depend on the gradients of the boundary layer component. In the case of an exponential boundary layer, when calculating a derivative of any arbitrarily given order, error estimates that are uniform with respect to a small parameter are obtained. The results of numerical experiments are presented. [ABSTRACT FROM AUTHOR] |
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