
Accession Number : AD0601107
Title : APPLICATION OF THE GALERKIN METHOD TO SELFADJOINT, NONPOSITIVE DEFINITE EIGENVALUE PROBLEMS IN HYDRODYNAMIC STABILITY,
Corporate Author : RENSSELAER POLYTECHNIC INST TROY N Y
Personal Author(s) : Tsao,Sherman
Report Date : 25 MAY 1964
Pagination or Media Count : 29
Abstract : The method of Galerkin for obtaining approximate eigenvalues is applied to a class of selfadjoint but not positive definite (Mdefinite) eigenvalue problems. The present investigation shows that the positive and negative approximate eigenvalues obtained from the Galerkin method are respectively the upper and lower bounds of the corresponding exact eigenvalues. It is also shown that the sequence of approximate eigenvalues obtained using successively more expansion functions converges monotonically to the exact eigenvalues. Finally a method for predetermining the signs of the approximate eigenvalues is given. As numerical examples of the theory, two Mdefinite eigenvalue problems arising from inviscid stability analyses of flows between concentric cylindrical surfaces are cnsidered. (Author)
Descriptors : (*HYDRODYNAMICS, NUMERICAL ANALYSIS), (*MATRICES(MATHEMATICS), HYDRODYNAMICS), FLUID FLOW, VISCOSITY, STABILITY, CYLINDRICAL BODIES, SURFACE PROPERTIES, BOUNDARY VALUE PROBLEMS, FUNCTIONS(MATHEMATICS), EQUATIONS
Distribution Statement : APPROVED FOR PUBLIC RELEASE