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Simple Singular Perturbation Problems with Turning Points

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DOI: 10.4236/jamp.2019.712208    56 Downloads   131 Views


The paper considers the asymptotic solution of two-point boundary value problems εy” + A(x)y’ = 0, 0 ≤ x ≤ 1, when 0 < ε ? 1, A(x) is smooth with isolated zeros, y(0) = 0 and y(1) = 1. By using perturbation method, the limit asymptotic solutions of various cases are obtained. We provide a reliable and direct method for solving similar problems. The limiting solutions are constants in this paper, except in narrow boundary and interior layers of nonuniform convergence. These provide simple examples of boundary layer resonance.

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Wang, N. (2019) Simple Singular Perturbation Problems with Turning Points. Journal of Applied Mathematics and Physics, 7, 2979-2989. doi: 10.4236/jamp.2019.712208.

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