Rosenbrock methods for differential algebraic equations
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Publication:1819549
DOI10.1007/BF01401021zbMath0613.65076OpenAlexW1991424184MaRDI QIDQ1819549
Publication date: 1988
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/133224
Rosenbrock methodsdifferential algebraic equationsTaylor expansionindex oneconvergent embedded methods
Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05)
Related Items (31)
Half-explicit Runge-Kutta methods for semi-explicit differential- algebraic equations of index 1 ⋮ (m, k)-schemes for stiff systems of ODEs and DAEs ⋮ Numerical event location techniques in discontinuous differential algebraic equations ⋮ Two-dimensional fully adaptive solutions of reaction-diffusion equations ⋮ A Survey on Numerical Methods for the Simulation of Initial Value Problems with sDAEs ⋮ A note on stability investigations for Rosenbrock-type methods for quasilinear-implicit differential equations ⋮ A composition law for Runge-Kutta methods applied to index-2 differential-algebraic equations ⋮ The behaviour of the local error in splitting methods applied to stiff problems ⋮ The application of Rosenbrock-Wanner type methods with stepsize control in differential-algebraic equations ⋮ Error of Rosenbrock methods for stiff problems studied via differential algebraic equations ⋮ Adaptive FEM for reaction-diffusion equations ⋮ Generalized ROW-type methods for solving semi-explicit DAEs of index-1 ⋮ Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems ⋮ Dense output for extrapolation methods ⋮ High order accurate, one-sided finite-difference approximations to concentration gradients at the boundaries, for the simulation of electrochemical reaction-diffusion problems in one-dimensional space geometry. ⋮ Continuous extensions of Rosenbrock-type methods ⋮ Construction of Rosenbrock-Wanner method Rodas5p and numerical benchmarks within the Julia differential equations package ⋮ On error behaviour of partitioned linearly implicit Runge-Kutta methods for stiff and differential algebraic systems ⋮ Improvement of Rosenbrock-Wanner Method RODASP ⋮ Rosenbrock-type methods applied to finite element computations within finite strain viscoelasticity ⋮ Rosenbrock-type methods applied to discontinuous differential systems ⋮ Application of the rosenbrock methods to the solution of unsteady 3D incompressible Navier-Stokes equations ⋮ Krylov-ROW methods for DAEs of index 1 with applications to viscoelasticity ⋮ Rosenbrock methods for differential-algebraic systems with solution- dependent singular matrix multiplying the derivative ⋮ A class of linearly-implicit Runge-Kutta methods for multibody systems ⋮ A multirate ROW-scheme for index-1 network equations ⋮ Finite element analysis of viscoelastic structures using Rosenbrock-type methods ⋮ Two-dimensional cascadic finite element computations of combustion problems ⋮ Rosenbrock-Wanner Methods: Construction and Mission ⋮ Water and Hydrogen Flow in Networks: Modelling and Numerical Solution by ROW Methods ⋮ Chebyshev series approximation for solving differential–algebraic equations (DAEs)
Uses Software
Cites Work
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- One-step and extrapolation methods for differential-algebraic systems
- Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations
- A study of Rosenbrock-type methods of high order
- Instructive experiments with some Runge-Kutta-Rosenbrock methods
- ODE Methods for the Solution of Differential/Algebraic Systems
- Differential-Algebraic Systems as Differential Equations on Manifolds
- Order Results for Implicit Runge–Kutta Methods Applied to Differential/Algebraic Systems
- Differential/Algebraic Equations are not ODE’<scp>s</scp>
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