Numerical methods for eighth-, tenth- and twelfth-order eigenvalue problems arising in thermal instability
type: Item
instance of: scholarly article
title: Numerical methods for eighth-, tenth- and twelfth-order eigenvalue problems arising in thermal instability
zbMATH Open document ID: 0847.76057
DOI: 10.1007/BF02521607
author: E. H. Twizell
author: A. Boutayeb
author: K. Djidjeli
published in: Advances in Computational Mathematics
publication date: 1995-08-13T00:00:00Z
review text: The authors study the problem of an infinite horizontal layer of fluid of uniform thickness, heated from below, rotating uniformly and subject to a uniform magnetic field acting in the same direction as gravity. Instability considered as overstability may be modelled by an eigth-order ordinary differential equation. Taking into account the uniform magnetic field, the ordinary convection can be modelled by a tenth-order differential equation, while overstability can be described by a twelfth-order differential equation. Two methods are applied in all three cases. In the first approach, a direct second-order numerical method is developed by approximating the derivatives in the model differential equations by second-order finite differences. In the second approach, the differential equations are transformed into equivalent second-order systems, and well-known finite difference second-order and fourth-order methods are used to obtain eigenvalues. By comparing the results given by the present theory with those known from the literature, a very good agreement is observed.
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 76E25
Mathematics Subject Classification ID: 76E15
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 784503
zbMATH Keywords: rotating flow
zbMATH Keywords: infinite horizontal layer
zbMATH Keywords: uniform magnetic field
zbMATH Keywords: overstability
zbMATH Keywords: eigenvalues
reviewed by: Ioan Pop
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 784503