## 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.

## References

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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