Finite difference approximate solutions for the strongly damped extensible beam equations

DOI10.1016/S0096-3003(99)00005-3zbMath1026.74079OpenAlexW1998904091MaRDI QIDQ1569222

N. Delaunay

Publication date: 25 June 2000

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

Full work available at URL: https://doi.org/10.1016/s0096-3003(99)00005-3

zbMATH Keywords

stabilityexistencemethod of linesimplicit finite difference schemeenergy conservationdiscrete energy methodstrongly damped extensible beam equations

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Numerical approximation of solutions of dynamical problems in solid mechanics (74H15) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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)

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Cites Work

• Energy convergence results for strongly damped nonlinear wave equations
• \(L^2\)-error estimate for the strongly damped extensible beam equations
• Free vibrations and dynamic buckling of the extensible beam
• Stability theory for an extensible beam
• Initial-boundary value problems for an extensible beam
• The convergence of a Galerkin approximation scheme for an extensible beam
• Stability theory for quasi-linear wave equations with linear damping
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