Trouble might occur for instance when

*1)* the highest order derivative is multiplied by .

*2)* the problem totally changes characteristics when the parameter is equal to zero.

*3)* the problem is defined on infinite regions.

*4)* singular points are present.

*5)* the equation models physical processes with several time- or length scales.

*1-5* are called *singular perturbation problems*.

In many cases we deal with problem containing *boundary layers*. We can roughly treat these problems by

*i)* letting we get a good approximation for the outer region.

*ii)* rescale the problem to get an inner approximation.

*iii)* match inner and outer approximations.

Singular perturbation is *matched asymptotic expansion*.