Abstract

AbstractQuadrature formula for one variable functions with a boundary layer component is constructed and studied. It is assumed that the integrand can be represented as a sum of regular and boundary layer components. The boundary layer component has high gradients, therefore an application of Newton-Cotes quadrature formulas leads to large errors. An analogue of Newton-Cotes rule with five nodes is constructed. The error of the constructed formula does not depend on gradients of the boundary layer component. Results of numerical experiments are presented.Keywordsfunctionnumerical integrationboundary layer componentnonpolynomial interpolationquadrature ruleuniform accuracy

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