Delay Equations, Approximation and Application: International Symposium at the University of Mannheim, October 8–11, 1984

351 Pages·1985·7.86 MB·English

by  Günter Meinardus

ISNM74:
International Series of Numerical Mathematics
Internationale Schriftenreihe zur Numerischen Mathematik
Serie inteJ'llationaie d'A nalyse numerique
Vol. 74
Edited by
Ch. Blanc, Lausanne; R. Glowinski, Paris;
G. Golub, Stanford; P. Henrici, Ziirich;
H. O. Kreiss, Pasadena; A. Ostrowski, Montagnola;
J. Todd, Pasadena
Birkhauser Verlag
Basel· Boston· Stuttgart
Delay Equations,
Approximation
and Application
International Symposium at the
University of Mannheim,
October 8-11, 1984
Edited by
G. Meinardus
G. Nurnberger
1985 Birkhiiuser Verlag
Basel . Boston • Stuttgart
Editors
G. Meinardus G. Nurnberger
Universitiit Mannheim Universitiit Mannheim
Lehrstuhl fUr Mathematik IV Fakultiit fUr Mathematik
D-6800 Mannheim 1 und Informatik
D-6800 Mannheim
Supported by .,Stijtung Volkswagenwerk«
CIP·Kurztitelaufnahme der Deutsdlen Bibliotbek
Delay equations, approximation and application:
internat. symposium at the Univ. of Mannheim,
October 8-11,19841 ed. by G. Meinardus ;
G. Nurnberger. - Basel; Boston; Stuttgart: Birkhiiuser,
1985.
(International series of numerical mathematics ;
Vol. 74)
ISBN·13: 978·3·0348·7378·9 e-ISBN·13: 978·3·0348·7376-5
DOl: 10.1007/978·3·0348·7376·5
NE: Meinardus, Gunter [Hrsg.]; Universitiit (Mannheim);
GT
All rights reserved.
No part of this publication may be reproduced, stored in
a retrieval system, or transmitted in any form or by any means,
electronic, mechanical, photocopying, recording or otherwise,
without the prior permission of the copyright owner.
© 1985 Birkhiiuser Verlag Basel
Softcover reprint of the hardcover 1st edition 1985
5
CONTENTS
Preface ................•............................................•. 9
Participants ......•...........................•..........•.•.•....•... 11
G.Meinardus and G. Nurnberger
Approximation Theory and Numerical Methods for Delay Differential
Equations.......................................................... 13
H. Arndt, P.J. van der Houwen and B.P. Sommeijer
Numerical Integration of Retarded Differential Equations with
Periodic Solutions................................................. 41
A. Bellen
Constrained Mesh Methods for Functional Differential Equations......... 52
H.-P. Blatt and E.B. Saff
Distribution of Zeros of Polynomial Sequences, Especially
Best Approximations................................................ 71
B.D. Bojanov, Q.I. Rahman and J. Szynal
On a Conjecture about the Critical Points of a Polynomial.............. 83
L. Collatz
Inclusion of Solutions of Certain Types of Linear and Nonlinear
Delay-Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . • . . • . . . . 94
F.-J. Delvos
Interpolation of Odd Periodic Functions on Uniform Meshes.............. 105
F. Deutsch
Simultaneous Interpolation and Norm-Preservation....................... 122
6
B. Dreseler
Lebesgue Constants and Best Conditions for the Norm-Convergence
of Fourier Series................................................. 133
U. an der Heiden
Stochastic Properties of Simple Differential -
Delay Equations................................................... 147
Ch.L. Hu and L.L. Schumaker
Bivariate Natural Spline Smoothing.................................... 165
G. NUrnberger
Best Approximation by Spline Functions: Theory and
Numerical Methods................................................. 180
Q.I. Rahman and G. Schmeisser
Reconstruction and Approximation of Functions from Samples............ 213
W. Schempp
Time Delay and Doppler Frequency Shift in Radar/Sonar Detection,
with Application to Fourier Optics................................ 234
M. Sommer
Uniqueness of Best L1-Approximations of Continous Functions........... 264
H. Strauss
Comparison Theorems in Spline Approximation........................... 282
G.D. Taylor
The Differential Correction Algorithm....... .......................... 288
H. Werner and C. Fesser
Ein mathematisches Modell fUr den Reifungsprozess roter
Blutkorperchen bei Neugeborenen................................... 304
7
M. Zennaro
On the P-Stability of One-Step Collocation for Delay
Differential Equations........................................... 334
Some Open Problems.............................................. . . . . . 344
9
PREFACE
The international symposium held in October 1984 at the Uni
versity of Mannheim was the first with the special aim to expose
the connection of the Theory of Delay Eauations and Approximation
Theory with the emphasis on constructive methods and applications.
Although the separate character of both domains is reflected by
their historical development, the latest research shows that
the numerical treatment of Delay Equations leads to various appro
ximation and optimization problems. An introductory survey of
this circle of problems written by the editors is included at the
beginning of the book.
Delay Equations have their origin in domains of applications,
such as physics, engineering, biology, medicine and economics.
They appear in connection with the fundamental problem to analyse
a retarded process from the real world, to develop a corresponding
mathematical model and to determine the future behavior.
Thirty mathematicians attended the conference coming from
Germany, West- and Eastern Europe and the United States- more
than twenty of them presented a research talk.
The lectures about Delay Equations were mainly oriented on the
following subjects: single-step, multi-step and spline methods;
monotonicity methods for error estimations; asymptotic behavior
10
and periodicity of solutions. The topics of the talks on Approxi
mation Theory covered different aspects of approximation by poly
nomials, splines and rational functions and their numerical rea
lization. Additionally included in the scientific program was a
special session on Open Problems, where several suggestions were
made for further research concerning both fields.
The free and harmonic atmosphere which lasted during the whole
conference led to intensive and fruitful scientific discussions.
Our special thank is due to the "STIFTUNG VOLKSWAGENWERK" for
their generous financial support of the symposium. Moreover, we
would like to thank the "BIRKHXUSER-VERLAG" for the kind agree
ment to publish this volume.
Our hope is that this meeting will stimulate the experts from
Delay Equations and Approximation Theory to utilize the methods
from both domains for solving at least some of the open problems.
GUnter Meinardus GUnther NUrnberger