Order barriers for the B-convergence of ROW methods

DOI10.1007/BF02259094zbMath0662.65070MaRDI QIDQ1114353

S. H. Smith

Publication date: 1989

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

Rosenbrock methodsstiff differential equationsglobal errororder barriersProthero-Robinson problemB-convergence

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (20)

\(W\)-methods for semilinear parabolic equations ⋮ Error of Rosenbrock methods for stiff problems studied via differential algebraic equations ⋮ W-methods to stabilize standard explicit Runge-Kutta methods in the time integration of advection-diffusion-reaction PDEs ⋮ Generalized ROW-type methods for solving semi-explicit DAEs of index-1 ⋮ Rosenbrock-Wanner and W-methods for the Navier-Stokes equations ⋮ Design of DIRK schemes with high weak stage order ⋮ Algebraic Structure of the Weak Stage Order Conditions for Runge–Kutta Methods ⋮ Construction of Rosenbrock-Wanner method Rodas5p and numerical benchmarks within the Julia differential equations package ⋮ Improvement of Rosenbrock-Wanner Method RODASP ⋮ A New Stiffly Accurate Rosenbrock-Wanner Method for Solving the Incompressible Navier-Stokes Equations ⋮ An analysis of the Prothero-Robinson example for constructing new DIRK and ROW methods ⋮ On Rosenbrock methods for the time integration of nearly incompressible materials and their usage for nonlinear model reduction ⋮ A stiffly accurate Rosenbrock-type method of order 2 applied to FE-analyses in finite strain viscoelasticity ⋮ An improved class of generalized Runge-Kutta methods for stiff problems. II: The separated system case ⋮ The Prothero and Robinson example: convergence studies for Runge-Kutta and Rosenbrock-Wanner methods ⋮ Order reduction of stiff solvers at elastic multibody systems ⋮ Rosenbrock-Wanner Methods: Construction and Mission ⋮ Improved traditional Rosenbrock-Wanner methods for stiff ODEs and DAEs ⋮ A multirate W-method for electrical networks in state-space formulation ⋮ Spectral/Rosenbrock discretizations without order reduction for linear parabolic problems

Cites Work

• A study of Rosenbrock-type methods of high order
• Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
• The Concept of B-Convergence
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• A special family of Runge-Kutta methods for solving stiff differential equations
• Restricted Padé Approximations to the Exponential Function

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