Approximation of a Function and Its Derivatives on the Basis of Cubic Spline Interpolation in the Presence of a Boundary Layer

Blatov, I. A.; Задорин, А. И.; Kitaeva, E. V.

doi:10.1134/s0965542519030047

Cited by 6 publications

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“…In this case, the nodes of the spline itself do not change and coincide with the nodes of Ω. In accordance with [11], the following theorem is true.…”

Section: Shishkin Meshsupporting

confidence: 59%

“…Let us proceed to the analysis of this approach in the case when the function u(x) has large gradients and the decomposition ( 1) is valid for it. In accordance with [11], the following theorem is true.…”

Section: Shishkin Meshmentioning

confidence: 65%

“…Thus, for σ < 1 2 the grid Ω is uniform on the interval [σ, 1] with step h = 2(1 − σ)/N . In the region of the boundary layer, for 0 ≤ n ≤ N/2, the grid nodes in accordance with (11) are set in the form…”

Section: Bakhvalov Meshmentioning

confidence: 99%

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Analysis of approaches to spline interpolation of functions with large gradients in the boundary layer

Blatov

Задорин

2022

J. Phys.: Conf. Ser.

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The problem of cubic spline interpolation of functions with large gradients in the boundary layer is considered. It is assumed that the decomposition in the form of the sum of the regular and singular components is valid for the interpolated function. This decomposition is valid for the solution of a boundary value problem for a second order ordinary differential equation with a small parameter e at the highest derivative. An overview of approaches to the construction of splines, the error of which is uniform with respect to the small parameter e, is given. The approaches are based on the use of Shishkin and Bakhvalov meshes, which are thickened in the boundary layer region. An alternative approach based on a modification of a cubic spline with fitting to the singular component of the interpolated function is also considered. The comparison of the accuracy of the applied approaches with the performance of computational experiments is carried out.

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“…In this case, the nodes of the spline itself do not change and coincide with the nodes of Ω. In accordance with [11], the following theorem is true.…”

Section: Shishkin Meshsupporting

confidence: 59%

Section: Shishkin Meshmentioning

confidence: 65%