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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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An analysis of a uniformly accurate difference method for a singular perturbation problem
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by Alan E. Berger, Jay M. Solomon and Melvyn Ciment PDF
Math. Comp. 37 (1981), 79-94 Request permission

Abstract:

It will be proven that an exponential tridiagonal difference scheme, when applied with a uniform mesh of size h to: $\varepsilon {u_{xx}} + b(x){u_x} = f(x)$ for $0 < x < 1,b > 0$, b and f smooth, $\varepsilon$ in (0, 1], and $u(0)$ and $u(1)$ given, is uniformly second-order accurate (i.e., the maximum of the errors at the grid points is bounded by $C{h^2}$ with the constant C independent of h and $\varepsilon$). This scheme was derived by El-Mistikawy and Werle by a ${C^1}$ patching of a pair of piecewise constant coefficient approximate differential equations across a common grid point. The behavior of the approximate solution in between the grid points will be analyzed, and some numerical results will also be given.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 79-94
  • MSC: Primary 65L10
  • DOI: https://doi.org/10.1090/S0025-5718-1981-0616361-0
  • MathSciNet review: 616361