A review on singularly perturbed differential equations with turning points and interior layers. (English) Zbl 1302.34087
Summary: Singular perturbation problems with turning points arise as mathematical models for various physical phenomena. The problem with interior turning point represent one-dimensional version of stationary convection-diffusion problems with a dominant convective term and a speed field that changes its sign in the catch basin. Boundary turning point problems, on the other hand, arise in geophysics and in modeling thermal boundary layers in laminar flow. In this paper, we review some existing literature on asymptotic and numerical analysis of singularly perturbed turning point and interior layer problems. The purpose is to find out what problems are treated and what numerical/asymptotic methods are employed, with an eye towards the goal of developing general methods to solve such problems. Since major work in this area started after 1970 so this paper limits its coverage to the work done by numerous researchers between 1970 and 2011.
MSC:
| 34E15 | Singular perturbations for ordinary differential equations |
| 34E20 | Singular perturbations, turning point theory, WKB methods for ordinary differential equations |
| 65L11 | Numerical solution of singularly perturbed problems involving ordinary differential equations |
Keywords:
singular perturbation; turning points; discontinuous data; ordinary differential equations; partial differential equations; asymptotic analysis; numerical analysisReferences:
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