Direct time integration algorithm with controllable numerical dissipation for structural dynamics: two-step lambda method

DOI10.1016/j.apnum.2009.12.005zbMath1192.65098OpenAlexW1999396315MaRDI QIDQ969319

V. A. Leontyev

Publication date: 6 May 2010

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2009.12.005

zbMATH Keywords

algorithmsconvergencenumerical examplescontrollable numerical dissipationstructural dynamicsL-stabilitysolid dynamicsgeneral multi-step integration methodshigh-frequency dampinghigh-oscillatory stiff ODElambda integration methodmaximal damping of high-frequency accelerationsunconditionally stable integration methods

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)

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Uses Software

• RODAS

Cites Work

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• Dahlquist's classical papers on stability theory
• A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method
• A Pre´cis of Developments in Computational Methods for Transient Analysis
• Extension of LMS formulations for L-stable optimal integration methods with U0–V0 overshoot properties in structural dynamics: the level-symmetric (LS) integration methods
• An alpha modification of Newmark's method
• Order stars and stability theorems
• Design, analysis, and synthesis of generalized single step single solve and optimal algorithms for structural dynamics
• A special stability problem for linear multistep methods