An analogue of Newton-Cotes formula with four nodes for a function with a boundary-layer component
A.I. Zadorin, N.A. Zadorin
Keywords: one-variable function, boundary-layer component, high gradients, definite integral, non-polynomial interpolation, quadrature rule, error estimate
Abstract
The construction of the Newton-Cotes formulas is based on approximating an integrand by the Lagrange polynomial. The error of such quadrature formulas can be serious for a function with a boundary-layer component. In this paper, an analogue to the Newton-Cotes rule with four nodes is constructed. The construction is based on using non-polynomial interpolation that is accurate for a boundary layer component. Estimates of the accuracy of the quadrature rule, uniform on gradients of the boundary layer component, are obtained. Numerical experiments have been performed.
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