Numerical Methods for Ordinary Differential Equations Proceedings of
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1386 A. Sellen C.W. Gear E. Russo (Eds.)
Numerical Methods for Ordinary Differential Equations Proceedings of the Workshop held in L'Aquila (Italy), Sept. 16-18, 1987
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Editors
Alfredo Bellen Dipartimento di Scienze Matematiche, Universita di Trieste 34100 Trieste, Italy Charles W. Gear Department of Computer Science, University of Illinois Urbana, lL 61801, USA Elvira Russo Dipartimento di Informatica e Applicazioni, Universita di Salerno 84100 Salerno, Italy
Mathematics Subject Classification (1980): 65L05, 65J 05,65005, 65W05,65M99 ISBN 3-540-51478-3 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-51478-3 Springer-Verlag New York Berlin Heidelberg
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INTRODUCTION. The theory of the numerical integration of initial value problems is by now classical. This theory has formed the basis for a spectrum of good codes for stiff and non stiff problems that enable users of conventional serial computers to solve the majority of problems with no great difficulty or inefficiency. Consequently, the thrust of much current research has been to extend the classical results to more general cases, especially to enable the application of ODE methods to problems such as those arising from PDEs by the application of the method of lines, a method that is particularly easy to apply in an automatic code, and to the differential-algebraic, integral, and delay equations that frequently arise in computer modeling of physical systems. As the number of users increases as well as their need for the accurate and rapid solution of the larger and larger systems that can be generated automatically with today's computer systems, two other important thrusts emerge. One is the improvement of codes to meet the needs of professionals in other disciplines who do not wish to be concerned with technical details of numerical methods. The second is the development of ODE methods suitable for the emerging generations of parallel computers. The purpose of the symposium on Ordinary Differential Equations organized by A.Bellen, A.Pasquali, L.Pasquini, E.Russo and D.Trigiante at the University of L'Aquila, Italy on September 16-18, 1987 was to examine some of these new developments and to explore the connections betweeen the classical background and new res
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