Strong Uniform Approximation for Some Singularly Perturbed Differential Equations Arising in Chemical Reactor Theory

Dialla Konate

Abstract: A family of singularly perturbed ordinary differential problems that arise from Chemical Reactor Theory introduced among others by O'Malley is under consideration. The numerical stability of this problem is very fragile, very sensitive to the functional space setting particularly to the norm the functional space is equipped with. So the issue of finding an asymptotic solution remains of higher interest since most of those one may find in the literature are not easy to compute or are not of higher order. What we do within the current paper is to make a repeated use of the classical matching technique that is well-known in Asymptotic Analysis to construct, via a strong stable corrector (in a sense to be defined) an easy to compute regular asymptotic solution of any pescribed order. This higher order solution is valid throughtout the geometric domain of study.

Keywords: singular perturbation; strong (stable) asymptotic expansion; boundary layer; strong stable corrector.

Classification (MSC2000): 34A45, 34A50, 34D15, 34E10, 65D.

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