article

One-step and extrapolation methods for differential- algebraic systems

Authors:

P. Deufhard,

E. Hairer,

J. ZugckAuthors Info & Claims

Numerische Mathematik, Volume 51, Issue 5

Pages 501 - 516

https://doi.org/10.1007/BF01400352

Published: 01 October 1987 Publication History

Abstract

No abstract available.

Cited By

View all

Le Coënt ABarbot BPekergin NGüzeliş C(2023)Bayesian Networks as Approximations of Biochemical NetworksComputer Performance Engineering and Stochastic Modelling10.1007/978-3-031-43185-2_15(216-233)Online publication date: 20-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-43185-2_15
Jax TSteinebach G(2017)Generalized ROW-type methods for solving semi-explicit DAEs of index-1Journal of Computational and Applied Mathematics10.1016/j.cam.2016.08.024316:C(213-228)Online publication date: 15-May-2017
https://dl.acm.org/doi/10.1016/j.cam.2016.08.024
Lotz JNaumann UHannemann-Tamas RPloch TMitsos A(2015)Higher-order Discrete Adjoint ODE Solver in C++ for Dynamic OptimizationProcedia Computer Science10.1016/j.procs.2015.05.23751:C(256-265)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1016/j.procs.2015.05.237
Show More Cited By

Index Terms

One-step and extrapolation methods for differential- algebraic systems
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations

Recommendations

Fractional step methods for index-1 differential-algebraic equations

In the numerical solution of ordinary differential systems, the method of fractional steps (also known as operator splitting) yields high-order accurate schemes based on separate, computationally convenient treatments of distinct physical effects. Such ...
Extrapolation methods for dynamic partial differential equations

Several extrapolation procedures are presented for increasing the order of accuracy in time for evolutionary partial differential equations. These formulas are based on finite difference schemes in both the spatial and temporal directions. One of these ...
Linearly implicit extrapolation methods for differential-algebraic systems

We consider the numerical solution of implicit differential equations in which the solution derivative appears multiplied by a solution-dependent singular matrix. We study extrapolation methods based on two linearly implicit Euler discretizations. Their ...

Comments

Information & Contributors

Information

Published In

Numerische Mathematik Volume 51, Issue 5

October 1, 1987

111 pages

ISSN:0029-599X

Editor:
F. L. Bauer

Issue’s Table of Contents

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 October 1987

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

24
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 11 Aug 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Le Coënt ABarbot BPekergin NGüzeliş C(2023)Bayesian Networks as Approximations of Biochemical NetworksComputer Performance Engineering and Stochastic Modelling10.1007/978-3-031-43185-2_15(216-233)Online publication date: 20-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-43185-2_15
Jax TSteinebach G(2017)Generalized ROW-type methods for solving semi-explicit DAEs of index-1Journal of Computational and Applied Mathematics10.1016/j.cam.2016.08.024316:C(213-228)Online publication date: 15-May-2017
https://dl.acm.org/doi/10.1016/j.cam.2016.08.024
Lotz JNaumann UHannemann-Tamas RPloch TMitsos A(2015)Higher-order Discrete Adjoint ODE Solver in C++ for Dynamic OptimizationProcedia Computer Science10.1016/j.procs.2015.05.23751:C(256-265)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1016/j.procs.2015.05.237
Arnold MBrüls OCardona A(2015)Error analysis of generalized- α Lie group time integration methods for constrained mechanical systemsNumerische Mathematik10.1007/s00211-014-0633-1129:1(149-179)Online publication date: 1-Jan-2015
https://dl.acm.org/doi/10.1007/s00211-014-0633-1
Constantinescu ESandu A(2013)Extrapolated Multirate Methods for Differential Equations with Multiple Time ScalesJournal of Scientific Computing10.1007/s10915-012-9662-z56:1(28-44)Online publication date: 1-Jul-2013
https://dl.acm.org/doi/10.1007/s10915-012-9662-z
Kassiotis CIbrahimbegovic ANiekamp RMatthies H(2011)Nonlinear fluid---structure interaction problem. Part IComputational Mechanics10.1007/s00466-010-0545-647:3(305-323)Online publication date: 1-Mar-2011
https://dl.acm.org/doi/10.1007/s00466-010-0545-6
Kulikov GShindin S(2005)Global Error Estimation and Extrapolated Multistep Methods For Index 1 Differential-Algebraic SystemsBIT10.1007/s10543-005-0014-345:3(517-542)Online publication date: 1-Sep-2005
https://dl.acm.org/doi/10.1007/s10543-005-0014-3
Kværnø A(2004)Singly Diagonally Implicit Runge–Kutta Methods with an Explicit First StageBIT10.1023/B:BITN.0000046811.70614.3844:3(489-502)Online publication date: 1-Aug-2004
https://dl.acm.org/doi/10.1023/B%3ABITN.0000046811.70614.38
Schlegel MMarquardt WEhrig RNowak U(2004)Sensitivity analysis of linearly-implicit differential-algebraic systems by one-step extrapolationApplied Numerical Mathematics10.1016/j.apnum.2003.07.00148:1(83-102)Online publication date: 1-Jan-2004
https://dl.acm.org/doi/10.1016/j.apnum.2003.07.001
Çelık EBayram M(2004)Numerical solution of differential-algebraic equation systems and applicationsApplied Mathematics and Computation10.1016/S0096-3003(03)00719-7154:2(405-413)Online publication date: 1-Jul-2004
https://dl.acm.org/doi/10.1016/S0096-3003%2803%2900719-7
Show More Cited By

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

Cited By

Index Terms

Recommendations

Fractional step methods for index-1 differential-algebraic equations

Extrapolation methods for dynamic partial differential equations

Linearly implicit extrapolation methods for differential-algebraic systems

Comments

Information

Published In

Publisher

Publication History

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations