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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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A mollifier useful for approximations in Sobolev spaces and some applications to approximating solutions of differential equations
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by Stephen Hilbert PDF
Math. Comp. 27 (1973), 81-89 Request permission

Abstract:

For a given uniform grid of ${E^N}$ (N-dimensional Euclidean space) with mesh h, a class of smoothing functions (mollifiers) is constructed. If a function is an element of the Sobolev space $H_2^m$, then the error made by replacing the given function by a smoother $({C^\infty })$ function (which is the given function convolved with one of the mollifiers) is bounded by a constant times ${h^m}$. This result is used to construct approximations for functions using Hermite or spline interpolation, even though the function to be approximated need not satisfy the continuity conditions necessary for the existence of a Hermite or spline interpolate. These techniques are used to find approximations to the generalized solution of a second order elliptic Neumann problem.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Math. Comp. 27 (1973), 81-89
  • MSC: Primary 65D10; Secondary 65N99
  • DOI: https://doi.org/10.1090/S0025-5718-1973-0331715-3
  • MathSciNet review: 0331715