Paper Info
Title
On the attainable order of collocation methods for the neutral functional-differential equations with proportional delays
Abstract
In this paper, we extend the recent results of H. Brunner in BIT (1997) for the DDE y′(t)= by(qt), y(0)=1 and the DVIE y(t)=1+∫0 t by(qs)ds with proportional delay qt, 0q≤1, to the neutral functional-differential equation (NFDE): and the delay Volterra integro-differential equation (DVIDE) : with proportional delays p i t and q i t, 0p i ,q i ≤1 and complex numbers a,b i and c i . We analyze the attainable order of m-stage implicit (collocation-based) Runge-Kutta methods at the first mesh point t=h for the collocation solution v(t) of the NFDE and the `iterated collocation solution u it (t)' of the DVIDE to the solution y(t), and investigate the existence of the collocation polynomials M m (t) of v(th) or M^ m (t) of u it (th), t∈[0,1] such that the rational approximant v(h) or u it (h) is the (m,m)-Padé approximant to y(h) and satisfies |v(h)−y(h)|=O(h 2 m +1). If they exist, then we actually give the conditions of M m (t) and M^ m (t), respectively.
Year
DOI
Venue
2000
10.1007/s006070050044
Computing
Keywords
DocType
Volume
AMS Subject Classifications: 65R20,45L10,34K99.,Key Words: Neutral functional-differential and delay Volterra integro-differential equation,proportional delay,collocation and iterated collocation method,Padé approximant,attainable order.
Journal
64
Issue
ISSN
Citations 
3
0010-485X
6
PageRank 
References 
Authors
1.46
1
1
Name
Order
Citations
PageRank
Emiko Ishiwata1349.71