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Finite difference approximate solutions for the strongly damped extensible beam equations. (English) Zbl 1026.74079
Summary: We obtain approximate solutions for strongly damped extensible beam equations using the method of lines and an implicit finite difference scheme. Existence and stability of the corresponding methods are studied, and error estimates are also obtained. Energy conservation and decay properties of finite difference approximate solutions are shown using the discrete energy method. Numerical results are also given in order to check the properties of analytical solutions.

MSC:
74S20 Finite difference methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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