The Prothero and Robinson example: convergence studies for Runge-Kutta and Rosenbrock-Wanner methods

DOI10.1016/j.apnum.2016.04.012zbMath1346.65038OpenAlexW2347921496MaRDI QIDQ739015

Joachim Rang

Publication date: 16 August 2016

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2016.04.012

zbMATH Keywords

stabilitynumerical exampleconsistencyerror boundsRunge-Kutta methodsRosenbrock-Wanner methodsone-step methodorder reduction\(B\)-convergenceexample of Prothero-Robinson

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (7)

High-order linearly implicit two-step peer schemes for the discontinuous Galerkin solution of the incompressible Navier-Stokes equations ⋮ Rosenbrock-Wanner and W-methods for the Navier-Stokes equations ⋮ 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 ⋮ Application of the rosenbrock methods to the solution of unsteady 3D incompressible Navier-Stokes equations ⋮ An analysis of the Prothero-Robinson example for constructing new adaptive ESDIRK methods of order 3 and 4

Uses Software

• ROS3P
• RODAS

Cites Work

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• Embedded SDIRK-methods of basic order three
• Order barriers for the B-convergence of ROW methods
• B-convergence: A survey
• Quasi stage order conditions for SDIRK methods
• A stiffly accurate Rosenbrock-type method of order 2 applied to FE-analyses in finite strain viscoelasticity
• An analysis of the Prothero-Robinson example for constructing new DIRK and ROW methods
• Improved traditional Rosenbrock-Wanner methods for stiff ODEs and DAEs
• New Rosenbrock W-methods of order 3 for partial differential algebraic equations of index
• Rosenbrock Methods for Partial Differential Equations and Fractional Orders of Convergence
• Stability Properties of Implicit Runge–Kutta Methods
• The Concept of B-Convergence
• Runge-Kutta Methods for Partial Differential Equations and Fractional Orders of Convergence
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems
• Linearly implicit time discretization of non-linear parabolic equations
• A New Stiffly Accurate Rosenbrock-Wanner Method for Solving the Incompressible Navier-Stokes Equations
• A-Stable Methods and Padé Approximations to the Exponential
• On Runge-Kutta processes of high order
• A special stability problem for linear multistep methods
• ROS3P -- An accurate third-order Rosenbrock solver designed for parabolic problems

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