Asymptotic algorithms critical case

It turns out that under suitable conditions, the asymptotics for both the initial value problem and the boundary value problem in the critical case have the same form as in Sections II.B and III.A. In particular, the solution of the initial value problem approaches one of the solutions of the reduced equation in the limit as /x. 0. But the algorithm for constructing the asymptotic expansion undergoes some changes. 

The algorithm for constructing the asymptotics for the solution of system (7.31) is in many ways similar to the algorithm for the system of ordinary differential equations in the critical case described in Section IV. 

For the first order, we have , = 0, and is an arbitrary function. At the next step of the asymptotic algorithm, we obtain (a typical situation for problems in the critical case) the equation for the as yet unknown function... 

Asymptotic [58] and worst case [65] analysis of online algorithms received very little attention so far within the DDM context. These approaches are criticized for being applicable only to very simple models and asymptotic analysis is further criticized for being valid only for a large number of jobs. However,... 

---