An analysis of the Prothero-Robinson example for constructing new DIRK and ROW methods

DOI10.1016/j.cam.2013.09.062zbMath1302.65179OpenAlexW2086621038MaRDI QIDQ2252354

Joachim Rang

Publication date: 17 July 2014

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2013.09.062

zbMATH Keywords

Navier-Stokes equationsnumerical examplesdifferential-algebraic equationsdiagonally implicit Runge-Kutta methodsRosenbrock-Wanner methodsorder reductionRosenbrock-type methodsProthero-Robinson example

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for differential-algebraic equations (65L80)

Related Items

A comparison of Rosenbrock and ESDIRK methods combined with iterative solvers for unsteady compressible flows, 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, Robustness and efficiency of an implicit time-adaptive discontinuous Galerkin solver for unsteady flows, Comparison of ROW, ESDIRK, and BDF2 for unsteady flows with the high-order flux reconstruction formulation, Design of DIRK schemes with high weak stage order, Algebraic Structure of the Weak Stage Order Conditions for Runge–Kutta Methods, Time adaptive numerical solution of a highly non-linear degenerate cross-diffusion system arising in multi-species biofilm modelling, A New Stiffly Accurate Rosenbrock-Wanner Method for Solving the Incompressible Navier-Stokes Equations, The Prothero and Robinson example: convergence studies for Runge-Kutta and Rosenbrock-Wanner methods, A parallel fourth order Rosenbrock method: construction, analysis and numerical comparison, Rosenbrock-Wanner Methods: Construction and Mission, Nonlinear \(p\)-multigrid preconditioner for implicit time integration of compressible Navier-Stokes equations with \(p\)-adaptive flux reconstruction, Improved traditional Rosenbrock-Wanner methods for stiff ODEs and DAEs, An analysis of the Prothero-Robinson example for constructing new adaptive ESDIRK methods of order 3 and 4

Uses Software

• MooNMD
• ROS3P
• UMFPACK
• RODAS

Cites Work

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