Singular perturbation

Summary

A problem with a small parameter $\varepsilon$ is singularly perturbed when setting $\varepsilon = 0$ does not give a uniformly good approximation of its solutions. A typical cause is a small parameter in front of the highest derivative. Then the reduced equation has lower order and cannot meet all boundary or initial conditions. The solutions then change rapidly in thin regions, such as boundary layers. Singular perturbations appear in fluid flow at high Reynolds number, chemical kinetics and slow-fast systems.