New Rosenbrock W-methods of order 3 for partial differential algebraic equations of index

DOI10.1007/s10543-005-0035-yzbMath1093.65097OpenAlexW2047725321MaRDI QIDQ2490364

Joachim Rang, Lutz Angermann

Publication date: 2 May 2006

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-005-0035-y

zbMATH Keywords

convergenceNavier-Stokes equationsnumerical examplesdifferential-algebraic equationsnonlinear parabolic equationsRosenbrock methodsorder reductionpartial differential-algebraic equations

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Implicit ordinary differential equations, differential-algebraic equations (34A09) Navier-Stokes equations (35Q30) Partial functional-differential equations (35R10) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical methods for differential-algebraic equations (65L80)

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Uses Software

• MooNMD
• ROS3P
• VODE
• DASSL
• RODAS
• ROWMAP

Cites Work

• Rosenbrock methods for differential-algebraic systems with solution- dependent singular matrix multiplying the derivative
• MooNMD -- a program package based on mapped finite element methods
• ROWMAP -- a ROW-code with Krylov techniques for large stiff ODEs
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• Perturbation index of linear partial differential-algebraic equations
• A class of low order DIRK methods for a class of DAEs
• The numerical solution of differential-algebraic systems by Runge-Kutta methods
• Implicit Runge–Kutta Methods for Differential Algebraic Equations
• VODE: A Variable-Coefficient ODE Solver
• An Attempt to Avoid Exact Jacobian and Nonlinear Equations in the Numerical Solution of Stiff Differential Equations
• A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems
• Exponential Integrators for Large Systems of Differential Equations
• Reference values for drag and lift of a two‐dimensional time‐dependent flow around a cylinder
• Linearly implicit time discretization of non-linear parabolic equations
• Numerical Solution of the Navier-Stokes Equations
• ROS3P -- An accurate third-order Rosenbrock solver designed for parabolic problems
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