By Arieh Iserles

Acta Numerica has tested itself because the top discussion board for the presentation of definitive reports of numerical research issues. Highlights of this year's factor comprise articles on sequential quadratic programming, mesh adaption, unfastened boundary difficulties, and particle equipment in continuum computations. The invited papers will permit researchers and graduate scholars alike to speedy grab the present traits and advancements during this box.

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**Sample text**

The convergent power series expansions are essentially replaced by asymptotic expansions and somewhat more work must be done to determine appropriate values for the integer N, if it exists in a given case. The use of one-step difference schemes up to the singular point, as in de Hoog and Weiss [11], may also be used in many cases. Calculations on such problems are performed very often but theoretical studies along the above indicated lines are just now in progress. 2. 2. oo-intervals; irregular singular points.

Then Q(t) is nonsingular for all t ^ r 0 . Proof. 22a,b,c), for t ^ f 0 , Further recall that C + P" 1 = (Iq x ,, 0, x p) since PP~* = /.

8). We note that Then, assuming BVh(Q) is stable, Aj,0) is nonsingular with So we can write Denote the block structure of A{,orl by where the Z$ are n x n matrices, 0 ^ 7, k ^ J. Now we have the form where This follows from the fact that &(h°\Zf) = I. In particular then, B^Z^ + BjP'Zff = o0kl and JS^ZJJ* = 0, 1 ^ j ^ J, 0 ^ k ^ J. Note that the column of blocks {Zjo^o is just the difference approximation, using BVh(Q\ to y <0) (/). 1. Thus Qtl0 is nonsingular for h0 sufficiently small and so is Aj,1'.