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Characterizing Computable Analysis with Differential Equations

Manuel L. Campagnolo, Kerry Ojakian
2008 Electronical Notes in Theoretical Computer Science  
Bournez and Hainry 2006 [5] used a function algebra to characterize the twice continuously differentiable functions of Computable Analysis, restricted to certain compact domains.  ...  The functions of Computable Analysis are defined by enhancing the capacities of normal Turing Machines to deal with real number inputs.  ...  Recently, there has been a quest for characterizations of computability of real functions (in this paper, "computable" with no additional reference will always refer to Computable Analysis) based on alternative  ... 
doi:10.1016/j.entcs.2008.12.004 fatcat:bvmaynycpnetbi45zvb6fsapjq

A Study of the Applications of Analog Computers

V.P. Kodali
1967 IEEE Transactions on Industrial Electronics and Control Instrumentation  
Computer applications in solving partial differential equations are also discussed. Potential capabilities and limitations of this type of computer as an aid in research and analysis are given.  ...  An electronic analog computer is a tool for solving mathematical differential equations.  ...  The classification is based on the type of the differential equation, which characterizes the system.  ... 
doi:10.1109/tieci.1967.229550 fatcat:r23yagjog5bpnczextmqrsjzd4

Numerical simulation of electric signal in the cyber-physical immunosensor system on rectangular lattice in R package

A. Sverstiuk
2019 Scientific journal of the Ternopil national technical university  
The computer program «Numerical analysis of the electrical signal from the converter that characterizes the number of fluorescing pixels in the immunosensor on rectangular lattice using delayed differential  ...  lattice using delayed differential equations is presented.  ...  Computer simulation of electrical signal from converter of cyber-physical immunosensor system on rectangular lattice using differential equations with delay by means of R package is carried out.  ... 
doi:10.33108/visnyk_tntu2019.02.096 fatcat:n7plnz7t7ve4vm7vdz5odvh25y

A Global Perspective on Applied Mathematics & Numerical Analysis

Aisan Khojasteh
2014 American Journal of Applied Mathematics  
Then expand my focus to a general account of what numerical analysis consists today.  ...  In this paper I examine numerical analysis what precisely it is and why it is important.  ...  differential equations.  ... 
doi:10.11648/j.ajam.20140202.15 fatcat:nvoqqxnkdret7dv2rcmmwzlabq

Introduction to the Special Issue on Numerical Methods for Differential and Integral Equations

Şuayip Yüzbaşı, Kamel Al-Khaled, Nurcan Baykuş Savaşaneril, Devendra Kumar
2020 CMES - Computer Modeling in Engineering & Sciences  
This problem is characterized by system of Navier Stokes equations which is a system of partial differential equations.  ...  These papers are interested in ordinary and partial differential equations, fractional differential equations, integral and integro-differential equations and some modelling problems.  ...  The stability analysis of the model is characterized by differential equation in the study. Also, a discrete fractional model is given by using the sense of Caputo fractional derivative.  ... 
doi:10.32604/cmes.2020.011225 fatcat:bdaougo3uvferm425zfe6whyba

Computability, Complexity and Programming with Ordinary Differential Equations

Olivier Bournez, Markus Bläser, Christophe Paul
2020 Symposium on Theoretical Aspects of Computer Science  
ordinary differential equation whose solutions can approximate any continuous function if provided with a suitable well-chosen initial condition.  ...  Ordinary Differential Equations (ODEs) appear to be a universally adopted and very natural way for expressing properties for continuous time dynamical systems.  ...  concepts from analysis, namely polynomial ordinary differential equations.  ... 
doi:10.4230/lipics.stacs.2020.3 dblp:conf/stacs/Bournez20 fatcat:gygty5y72nhdbkn2juzrlwtzym

System theoretic implications of numerical methods applied to the solution of ordinary differential equations

T. G. Windeknecht, H. D'angelo
1976 Proceedings of the June 7-10, 1976, national computer conference and exposition on - AFIPS '76  
This paper presents a system-theoretic analysis of numerical methods used in approximating solutions of ordinary differential equations.  ...  By representing ordinary differential equations with system block diagrams (Le., interconnections of static elements and integrators), a numerical method can be viewed as a process in which the integrators  ...  Much of the literature on the numerical analysis of ordinary differential equations deals with the problem of finding solutions to the class of differential equations defined by dXd~t) =f (x (t), t) (18a  ... 
doi:10.1145/1499799.1499932 dblp:conf/afips/WindeknechtD76 fatcat:fqqa5v2w2vhejky6amaozra5yq

Recursion Schemes, Discrete Differential Equations and Characterization of Polynomial Time Computations

Olivier Bournez, Arnaud Durand, Michael Wagner
2019 International Symposium on Mathematical Foundations of Computer Science  
of computability and complexity by classes of continuous ordinary differential equations.  ...  This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs).  ...  We consider here an original approach in between the two worlds: discrete oriented computation with differential equations.  ... 
doi:10.4230/lipics.mfcs.2019.23 dblp:conf/mfcs/BournezD19 fatcat:ettnqvdg7fdwnnhup7ueuspw2m

Error-analysis of hybrid computer loops

Elmer G. Gilbert
1967 Mathematics and Computers in Simulation  
facilitate the solution of the partial differential equation In applying sensitivity techniques to the DSDT characterizing field problems.  ...  differential equations has been described by the D] TOMOVIC, R. : <{ Sensitivity Analysis of Dynamic Sysauthor [6].  ... 
doi:10.1016/s0378-4754(67)80033-8 fatcat:5nzp6n543zcsrizy4f6anywu34

Page 3340 of Mathematical Reviews Vol. , Issue 91F [page]

1991 Mathematical Reviews  
Summary: “We describe a new method of numerical integration of ordinary differential equations with essentially inhomogeneous right sides on a multiprocessor computing machine with common instruction flow  ...  , differential algebraic equations (DAEs).  ... 

Proceedings of the international symposium on numerical analysis

1989 Journal of Computational and Applied Mathematics  
It emphasizes the technical aspects of the mathematical machinery needed in the analysis of programming languages and associated proof systems, including all non-trivial proofs.  ...  BOOK REVIEWS Program Correctness over Abstract Data Types, with Error-State Semantics This monograph presents an elaboration of Hoare-style program specification and verification in the presence of abstract  ...  Several characterizations of computability classes are given, exposing the sometimes intricate deviations from the standard theory over the natural numbers, as well as the relevancy with respect to the  ... 
doi:10.1016/0377-0427(89)90313-0 fatcat:pfjlnxzocrbw7ithxzjlwiwfwi

Page 3564 of Mathematical Reviews Vol. , Issue 90F [page]

1990 Mathematical Reviews  
The author considers the stability properties of numerical meth- ods for delay differential equations (DDEs) with respect to the 65 NUMERICAL ANALYSIS 3564 nonlinear test problem y’(t) = f(t, y(t), y(t—t  ...  {For the entire collection see MR 90a:00025.} 90f:65146 65L20 65L05 Torelli, Lucio (I-TRST) Stability of numerical methods for delay differential equations. J. Comput. Appl.  ... 

Program correctness over abstract data types, with error-state semantics

E. Van Gestel
1989 Journal of Computational and Applied Mathematics  
It emphasizes the technical aspects of the mathematical machinery needed in the analysis of programming languages and associated proof systems, including all non-trivial proofs.  ...  BOOK REVIEWS Program Correctness over Abstract Data Types, with Error-State Semantics This monograph presents an elaboration of Hoare-style program specification and verification in the presence of abstract  ...  Several characterizations of computability classes are given, exposing the sometimes intricate deviations from the standard theory over the natural numbers, as well as the relevancy with respect to the  ... 
doi:10.1016/0377-0427(89)90312-9 fatcat:fajj2c2ftra2bbklp4yd6ljuzy

Sensitivity and uncertainty quantification techniques applied to systems of conservation laws

James R. Kamm, William J. Rider, V. Gregory Weirs, Stefano Tarantola, Marco Ratto
2010 Procedia - Social and Behavioral Sciences  
Such techniques are typically employed either on data with poorly characterized underlying dynamics or on values from highly idealized model evaluations.  ...  We examine the application of these techniques to an intermediate case, in which data are generated from coupled, nonlinear partial differential equations-conservation laws-that admit discontinuous solutions  ...  Main text We examine the application of sensitivity analysis and uncertainty quantification techniques to study the behavior underlying the set of coupled, nonlinear partial differential equations (PDEs  ... 
doi:10.1016/j.sbspro.2010.05.179 fatcat:u2q726dbyzdj5mge5ylxipdxue

Robustness analysis and synthesis for nonlinear uncertain systems

Wei-Min Lu, J.C. Doyle
1997 IEEE Transactions on Automatic Control  
With the proposed NLMI characterizations, it is shown that the computation needed for robustness analysis and synthesis is not more difficult than that for checking Lyapunov stability; the numerical solutions  ...  A state-space characterization of robustness analysis and synthesis for nonlinear uncertain systems is proposed.  ...  Huang for her help with the implementation of the finite difference algorithm in Example V.2.  ... 
doi:10.1109/9.650015 fatcat:6do7gyglprgrhgxqkylew5hlbq
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