Book ChapterDOI
Quadrature Formula with Five Nodes for Functions with a Boundary Layer Component
A. I. Zadorin,Nikita Zadorin +1 more
- pp 540-546
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TLDR
Quadrature formula for one variable functions with a boundary layer component is constructed and an analogue of Newton-Cotes rule with five nodes is constructed, finding that the error of the constructed formula does not depend on gradients of the boundary Layer component.Abstract:
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 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 presentedread more
Citations
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Journal ArticleDOI
Lagrange interpolation and Newton-Cotes formulas for functions with boundary layer components on piecewise-uniform grids
TL;DR: In this article, the problem of interpolation of a one-variable function considered as a solution to a boundary value problem for an equation with a small parameter ǫ in the highest derivative is investigated.
Journal ArticleDOI
Analogue of Newton–Cotes formulas for numerical integration of functions with a boundary-layer component
A. I. Zadorin,N. A. Zadorin +1 more
TL;DR: In this article, the numerical integration of functions with a boundary-layer component whose derivatives are not uniformly bounded is investigated, and an analogue of Newton-Cotes formulas that is exact for the boundary layer component is constructed.
Journal ArticleDOI
Non-Polynomial Interpolation of Functions with Large Gradients and Its Application
A. I. Zadorin,N. A. Zadorin +1 more
TL;DR: In this article, an interpolation formula based on fitting to the component that defines the boundary-layer growth of the function is proposed, which can be used to construct formulas for numerical differentiation and integration and in the two-dimensional case.
Journal ArticleDOI
Modification of the Euler quadrature formula for functions with a boundary-layer component
TL;DR: The Euler quadrature formula for the numerical integration of functions with a boundary-layer component on a uniform grid is investigated in this paper, and it is proved that the resulting composite Euler formula is third-order accurate in space uniformly with respect to the boundary layer component and its derivatives.
References
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Book
Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions
TL;DR: Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems as mentioned in this paper, and the global errors in the numerical approximations are measured in the pointwise maximum norm.
Book
Numerical methods in scientific computing
Germund Dahlquist,Åke Björck +1 more
TL;DR: This book explains how to obtain and estimate accuracy in MATLAB multiple precision calculations and some of the techniques used in solving scalar nonlinear equations.
Book
Numerical Analysis and Its Applications
TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT, and the €(D) includes 7% for Germany, the€(A) includes 10% for Austria.