A note on solving the fourth-order parabolic equation by the sinc-Galerkin method. (English) Zbl 1327.65192
The author considers the beam equation of transverse oscillations in one space dimension, but due to the presence (along with the second-order time derivative) of a first-order time derivative there are other interpretations as well, like from shallow water waves. For this equation and initial and Dirichlet boundary conditions all details of the Galerkin method using sinc-functions are given. The approach (neglecting exponentially decaying terms) reduces the problem of the approximate solution to a Silvester equation for the coefficients of the sinc-interpolation in \(x\) and \(t\). 3 numerical examples are provided to demonstrate the fast convergence which, in one of the examples, is not hampered by a singularity of the right hand side function.
Reviewer: Gisbert Stoyan (Budapest)
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
beam equation; sinc-Galerkin method; transverse vibrations; Sivester equation; numerical example; convergenceReferences:
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