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Page 1001 of Mathematical Reviews Vol. 56, Issue 3 [page]

1978 Mathematical Reviews  
M. 7311 The syntax directed graph algorithm for the input of equations to the Taylor series system for solving ordinary differential equa- tions, Comput. J. 19 (1976), no. 4, 344-347. D.  ...  Zahar described [same J. 14 (1971), no. 3; 243-248; Zbl. 221 #65132] how the Taylor series method for the solution of the initial value problem of ordinary differential equations could be implemented as  ... 

Causal-Block Diagrams: A Family of Languages for Causal Modelling of Cyber-Physical Systems [chapter]

Cláudio Gomes, Joachim Denil, Hans Vangheluwe
2020 Foundations of Multi-Paradigm Modelling for Cyber-Physical Systems  
It describes the syntax and -both declarative and operational -semantics of CBDs incrementally.  ...  The description of a complex system in terms of constituent components and their interaction is one of the most natural and intuitive ways of decomposition.  ...  Partial support by the Flanders Make strategic research center for the manufacturing industry is also gratefully acknowledged.  ... 
doi:10.1007/978-3-030-43946-0_4 fatcat:lzwffecy5fcildhf5vggz6s3zi

Abstracts of Current Computer Literature

1971 IEEE transactions on computers  
(Ordinary) Integration of Differential Equations with Singularities 8425 Solution of Ordinary Differential Equations Using Lie Series 8426 see also Boundary Digital Model of Digital Network Structure  ...  A Program for Ordinary Differential Equations Using Lie-Series, H. Knapp and G. Wanner (U. Wisconsin, Madison); Rept.  ... 
doi:10.1109/t-c.1971.223248 fatcat:2h66e665r5gxvg6ikpxgsbnzqe

Book reports

2005 Computers and Mathematics with Applications  
Computers and Mathematics with Applications 49 (2005) 1585-1622 www.elsevier.com/locate/camwa BOOK REPORTS The Book Reports section is a regular feature of Computers ~ Mathematics with Applications.  ...  Ant Colony Optimization Algorithms for the Traveling Salesman Problem. 3.1 The Traveling Salesman Problem. 3.2 ACO Algorithms for the TSP. 3.3 Ant System and Its Direct Successors. 3.4 Extensions of Ant  ...  of Derivatives. 13.2.4 Convolution Theorem. 13.3 Green's Functions for Initial Value Problems for Ordinary Differential Equations. 13.4 A Signal Problem for the Wave Equation. 13.5 A Signal Problem for  ... 
doi:10.1016/j.camwa.2005.04.001 fatcat:melc2iqigrh6tn37ldct5k73jm

Model Checking Delay Differential Equations Against Metric Interval Temporal Logic

Peter Nazier Mosaad, Martin Fränzle, Bai Xue
2017 Scientific Annals of Computer Science  
We employ an over-approximation method based on interval Taylor series to enclose the solution of the DDE and thereby reduce the continuous-time verification problem for MITL formulae to a discrete-time  ...  Delay differential equations (DDEs) play an important role in the modeling of dynamic processes.  ...  The authors would like also to thank Ahmed Mahdi from University of Oldenburg for helpful discussions.  ... 
doi:10.7561/sacs.2017.1.77 fatcat:55prhu2rtndqldoruuzkrmluri

Modelica — A unified object-oriented language for physical systems modeling

Hilding Elmqvist
1997 Simulation Practice and Theory  
The short range goal was to design a modeling language for differential-algebraic equation systems with some discrete event features to handle discontinuities and sampled systems.  ...  Much of the Modelica syntax will be hidden from the end-user because, in most cases, a graphical user interface will be used to build models by selecting icons for model components, using dialogue boxes  ...  The authors are thankful for all the feedback that has been obtained from various people that have reviewed different versions of the design.  ... 
doi:10.1016/s0928-4869(97)84257-7 fatcat:thhwmtzlvnd3labq6ibsp3ezmq

Abstracts of Current Computer Literature

1970 IEEE transactions on computers  
A modified boundary condition is presented which is proved to be stable provided the differential equation is stable. 7890 The Solution in Chebyshev Series of Systems of Linear Differential Equations  ...  There has been no stable direct method for solving symmetric systems of linear equations which takes advantage of the symmetry.  ... 
doi:10.1109/t-c.1970.223037 fatcat:to2dda73zzh2jlyq3um6rpr3pe

NEWTON: An Interactive Environment for Exploring Mathematics

M.B. Hayden, E.A. Lamagna
1998 Journal of symbolic computation  
differential equations.  ...  Our system, called Newton, runs on Macintosh computers and consists of a user-friendly interface to the symbolic mathematics package Maple, supplemented by an extensive library of our own Maple code.  ...  Acknowledgements The authors would like to express their gratitude and appreciation to all the members of the Newton project over the years.  ... 
doi:10.1006/jsco.1997.0172 fatcat:h5bqo4g2p5ctdizt52v6n76qga

Automata-Based Model Counting for String Constraints [chapter]

Abdulbaki Aydin, Lucas Bang, Tevfik Bultan
2015 Lecture Notes in Computer Science  
For quantitative and probabilistic program analyses, checking the satisfiability of a constraint is not sufficient, and it is necessary to count the number of solutions.  ...  Our approach relies on the observation that, using an automata-based constraint representation, model counting reduces to path counting, which can be solved precisely.  ...  Our experiments on thousands of constraints extracted from real-world web applications demonstrates the effectiveness and efficiency of the proposed approach.  ... 
doi:10.1007/978-3-319-21690-4_15 fatcat:5tgzlhb4affarm5obclkwhazzq

Applications of real number theorem proving in PVS

Hanne Gottliebsen, Ruth Hardy, Olga Lightfoot, Ursula Martin
2012 Formal Aspects of Computing  
However the correctness of such tools is a cause for concern, as it is often the user's responsibility to ensure that input data meets all the side conditions required to justify the use of the algorithm  ...  part of the proof comprising a result in graph theory involving an analysis of millions of graphs.  ...  Parts of the work were sponsored by QinetiQ and DSTL, and we are grateful to them for financial support, the involvement, patience and insights they brought to the research, and for their suggestion of  ... 
doi:10.1007/s00165-012-0232-9 fatcat:cttlm47ehreezkk2ikywgwuixu

Automatic average-case analysis of algorithms

Philippe Flajolet, Bruno Salvy, Paul Zimmermann
1991 Theoretical Computer Science  
Many probabilistic properties of elementary discrete combinatorial structures of interest for the average-case analysis of 4gorithms prove to be decidable.  ...  (North-Holland) ' The name Lambda-Upsilon-Omega derives from the Greek verb root Atiw which means "I solve" and which is at the heart of the word arta-ly-.sis.  ...  Simplijica tion and resolution of equations (1) In the universe of purely iterative labelled structures, an equational definition of structures leads to a chain of equations that can be solved by direct  ... 
doi:10.1016/0304-3975(91)90145-r fatcat:yoecav3wjnhpnkc4z2tkoi42uu

Abstracts of Current Computer Literature

1969 IEEE transactions on computers  
Criteria in Oriented Graphs and Their Application to Com- puter Diagnosis 7142 -see also Error, Failures, Tests Differential Equations (Ordinary) Causes of Instabilities in the Numerical Integration  ...  This paper presents the causes of instabilities which arise during the numerical solution of ordinary differential equations.  ... 
doi:10.1109/t-c.1969.222584 fatcat:5xs4k4tnxzesrhzluh73ldlmy4

Solving Ordinary Differential Equations [chapter]

Svein Linge, Hans Petter Langtangen
2016 Programming for Computations - Python  
The present chapter starts with explaining how easy it is to solve both single (scalar) first-order ordinary differential equations and systems of first-order differential equations by the Forward Euler  ...  Differential equations constitute one of the most powerful mathematical tools to understand and predict the behavior of dynamical systems in nature, engineering, and society.  ...  That is, the differential equation gives a direct formula for the further direction of the solution curve.  ... 
doi:10.1007/978-3-319-32428-9_4 fatcat:ct72pxn26zgr5nvttnub3rciki

Solving Ordinary Differential Equations [chapter]

Svein Linge, Hans Petter Langtangen
2016 Programming for Computations - MATLAB/Octave  
The present chapter starts with explaining how easy it is to solve both single (scalar) first-order ordinary differential equations and systems of first-order differential equations by the Forward Euler  ...  Differential equations constitute one of the most powerful mathematical tools to understand and predict the behavior of dynamical systems in nature, engineering, and society.  ...  That is, the differential equation gives a direct formula for the further direction of the solution curve.  ... 
doi:10.1007/978-3-319-32452-4_4 fatcat:f45zmkhfkvd43esoasukvghkki

Lectures on Reduce and Maple at UAM I - Mexico [article]

Marc Toussaint
2001 arXiv   pre-print
These lectures give a brief introduction to the Computer Algebra systems Reduce and Maple. The aim is to provide a systematic survey of most important commands and concepts.  ...  Another emphasis is on the different implementations of tensor calculi and the exterior calculus by Reduce and Maple and their application in Gravitation theory and Differential Geometry.  ...  (Fuji Kako) TAYLOR multivariate Taylor series (Rainer Schpf) TPS univariate Taylor series with indefinite order (Alan Barnes, Julian Padget) WU Wu Algorithm for polynomial systems (Russell Bradford)  ... 
arXiv:cs/0105033v1 fatcat:um67ya34jff33meea3bcg2jlmi
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