Recent Advances in Computational and Applied Mathematics
This multi-author contributed proceedings volume contains recent advances in several areas of Computational and Applied Mathematics. Each review is written by well known leaders of Computational and Applied Mathematics. The book gives a comprehensive acco
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Theodore E. Simos Editor
Recent Advances in Computational and Applied Mathematics
Editor Theodore E. Simos Department of Mathematics College of Sciences King Saud University P.O. Box 2455 Riyadh 11451 Saudi Arabia and Laboratory of Computational Sciences Department of Computer Science and Technology University of Peloponnese 22100 Tripolis Greece [email protected]
ISBN 978-90-481-9980-8 e-ISBN 978-90-481-9981-5 DOI 10.1007/978-90-481-9981-5 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2010938640 Mathematics Subject Classification (2000): 65, 65D20, 65Rxx, 65Lxx, 30, 30G35, 31B05, 31B35, 31, 33C05, 33C10, 33C15, 35A08, 35G15, 35Q40, 35R01, 41A60, 49Jxx, 49Nxx, 76-xx, 76A05, 81Q05, 81Qxx, 93Exx © Springer Science+Business Media B.V. 2011 Chapter 10 was created within the capacity of an US governmental employment and therefore is in the public domain. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover design: WMXDesign Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This volume includes an exciting collection of papers on computational and applied mathematics presenting the recent advances in several areas of this field. All the papers have been peer reviewed by at least three reviewers. In the paper entitled: “Fifty Years of Stiffness” by Luigi Brugnano, Francesca Mazzia and Donato Trigiante a review on the evolution of stiffness is presented. The authors also given a precise definition of stiffness which encompasses all the previous ones. In the paper entitled: “Efficient Global Methods for the Numerical Solution of Nonlinear Systems of Two point Boundary Value Problems” by Jeff R. Cash and Francesca Mazzia, the authors investigated the numerical methods for the solution of nonlinear systems of two point boundary value problems in ordinary differential equations. More specifically they answer to the question: “which codes are currently available for solving these problems and which of these codes might we consider as being state of the art”. Finally the authors included some new codes for BVP’s which are written in MATLAB. These codes was not available before and allow us for the first time in the literature the possibility of comparing some important MATLAB codes for solving boundary value problems. In the paper entitled: “Advances on collocation based numerical methods for Ordinary Differential Equations and Volterra Integral Equations” by D. Conte, R. D’Ambrosio, B. Paternoster a survey on collocation based numerical methods for the numerical integration of Ordinary Differential Equations and Volterra Integral Equations (VIEs) is presented. This surv
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