Gauss quadrature on a piecewise uniform mesh for functions with large gradients in a boundary layer

Gauss quadrature for a function with large gradients in the exponential boundary layer is investigated. In the case of such function the application of Gauss formula on the uniform grid leads to significant errors. The accuracy of Gauss quadrature on Shishkin mesh is investigated. The error of the quadrature formula is estimated. This estimate is uniform with respect to the small parameter. Results of numerical experiments are discussed.