An \(L\)-stable Rosenbrock method for step-by-step time integration in structural dynamics.

DOI10.1016/0045-7825(95)00823-JzbMath1067.74596OpenAlexW2026232079WikidataQ127570797 ScholiaQ127570797MaRDI QIDQ1578691

Robert Piché

Publication date: 4 September 2000

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(95)00823-j

zbMATH Keywords

tangential stiffness matrix\(LU\) decomposition

Mathematics Subject Classification ID

Numerical approximation of solutions of dynamical problems in solid mechanics (74H15) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite difference methods applied to problems in solid mechanics (74S20)

Related Items (7)

Heterogeneous asynchronous time integrators for computational structural dynamics ⋮ Short time angular impulse response of Rayleigh beams ⋮ Unnamed Item ⋮ The GPL-stability of Rosenbrock methods for delay differential equation. ⋮ About the use of the HdHr algorithm group in integrating the movement equation with nonlinear terms ⋮ The TR-BDF2 method for second order problems in structural mechanics ⋮ GP-stability of Rosenbrock methods for system of delay differential equation

Uses Software

• Matlab
• RODAS
• ode23
• ode45
• Ode15s
• ode113
• ode23s
• MATLAB ODE suite

Cites Work

• Unnamed Item
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• Unnamed Item
• Extended comparison of the Hilber-Hughes-Taylor \(\alpha\)-method and the \(\Theta _ 1\)-method
• A family of single-step Houbolt time integration algorithms for structural dynamics
• Second derivative methods applied to implicit first- and second-order systems
• The methods of Gellert and of Brusa and Nigro are Padé approximant methods
• Some general implicit processes for the numerical solution of differential equations
• An Attempt to Avoid Exact Jacobian and Nonlinear Equations in the Numerical Solution of Stiff Differential Equations
• On some unconditionally stable, higher order methods for the numerical solution of the structural dynamics equations
• Implicit-Explicit Finite Elements in Transient Analysis: Implementation and Numerical Examples
• A class ofA-stable methods

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