Order results for Rosenbrock type methods on classes of stiff equations

DOI10.1007/BF01385806zbMath0753.65062OpenAlexW2049856163MaRDI QIDQ1183045

Mario Büttner, Rüdiger Weiner, Karl Strehmel

Publication date: 28 June 1992

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133575

zbMATH Keywords

singular perturbationstiff equationssemilinear problemsRosenbrock type methods\(B\)-convergencelinearly implicit Runge-Kutta methods\(B\)-consistency

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Singular perturbations for ordinary differential equations (34E15) Multiple scale methods for ordinary differential equations (34E13)

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Convergence results of two-step W-methods for two-parameter singular perturbation problems ⋮ \(W\)-methods for semilinear parabolic equations ⋮ Errors of linear multistep methods for singularly perturbed Volterra delay-integro-differential equations ⋮ High-order \(W\)-methods ⋮ Implicit-Explicit Runge-Kutta-Rosenbrock Methods with Error Analysis for Nonlinear Stiff Differential Equations ⋮ W-methods to stabilize standard explicit Runge-Kutta methods in the time integration of advection-diffusion-reaction PDEs ⋮ A robust fitted operator finite difference method for a two-parameter singular perturbation problem¹ ⋮ Error analysis of variable stepsize Runge-Kutta methods for a class of multiply-stiff singular perturbation problems ⋮ On the construction of restricted-denominator exponential W-methods ⋮ Some secant approximations for Rosenbrock \(W\)-methods ⋮ Convergence of linear multistep methods for two-parameter singular perturbation problems ⋮ Order results for Krylov-\(W\)-methods ⋮ Convergence of parallel multistep hybrid methods for singular perturbation problems

Cites Work

• Rosenbrock methods for stiff ODEs: A comparison of Richardson extrapolation and embedding technique
• On error behaviour of partitioned linearly implicit Runge-Kutta methods for stiff and differential algebraic systems
• Partitioned adaptive Runge-Kutta methods and their stability
• B-convergence results for linearly implicit one step methods
• Error of Rosenbrock methods for stiff problems studied via differential algebraic equations
• A study of Rosenbrock-type methods of high order
• Behandlung steifer Anfangswertprobleme gewöhnlicher Differentialgleichungen mit adaptiven Runge-Kutta-Methoden
• On the stability of semi-implicit methods for ordinary differential equations
• Rosenbrock Methods using few LU-Decompositions
• An Attempt to Avoid Exact Jacobian and Nonlinear Equations in the Numerical Solution of Stiff Differential Equations
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