On singular singularly perturbed initial value problems. (English) Zbl 0676.34038

Gu, Zhongmei; Nefedov, N. N.; O’Malley, Robert E. jun.

SIAM J. Appl. Math. 49, No. 1, 1-25 (1989).

The singular system \(\epsilon z'(t)=F(z,t,\epsilon)\) with a small \(\epsilon >0\) and give z(0) is solved under certain assumptions in a finite interval [0,T] up to an O(\(\epsilon)\) in the case that F(Z,t,0) has an infinite family of solutions Z(t). The investigation combines the methods of A. B. Vasileva and V. F. Butuzov [Singularly perturbed equations in the critical case, Moscow State Univ. (1978)] with those of R. E. O’Malley and J. E. Flaherty [SIAM J. Appl. Math. 38, 225-248 (1980; Zbl 0471.65056)] and simplifies them. Eight striking examples are given.

Reviewer: L.Berg

MSC:

34E15	Singular perturbations for ordinary differential equations
34E20	Singular perturbations, turning point theory, WKB methods for ordinary differential equations
34C45	Invariant manifolds for ordinary differential equations

Keywords:

stiff equations; asymptotic methods; examples

Citations:

Zbl 0471.65056