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The numerical integration of functions with a boundary-layer component whose derivatives are not uniformly bounded is investigated. The Newton–Cotes formulas as applied to such functions can lead to… (More)

Quadrature formulas for one-variable functions with a boundary-layer component are constructed and studied. It is assumed that the integrand can be represented as the sum of a regular and a… (More)

A two-grid method for the elliptic equation with a small parameter e multiplying the highest derivative is investigated. The difference schemes with the property of e-uniform convergence on a uniform… (More)

The construction of the Newton-Cotes formulas is based on approximating the integrand by a Lagrange polynomial. The error of such quadrature formulas can be great for a function with a boundary-layer… (More)

- Alexander Zadorin, Nikita Zadorin
- NAA
- 2012

Quadrature 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… (More)

Spline interpolation of functions of one variable with a boundary-layer component is examined. Functions of this type can arise in the solution of a singularly perturbed boundary value problem on an… (More)

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