Accession Number : AD0671529

Title :   AN APPLICATION OF THE EXTENDED KANTOROVICH METHOD TO EIGENVALUE PROBLEMS,

Corporate Author : NEW YORK UNIV N Y DEPT OF AERONAUTICS AND ASTRONAUTICS

Personal Author(s) : Kerr,Arnold D.

Report Date : DEC 1967

Pagination or Media Count : 25

Abstract : The paper presents the application of the extended Kantorovich method to solve eigenvalue problems in partial differential equations. The specific examples treated are: the vibrations of a rectangular membrane and the stability of an elastic rectangular plate compressed in its plane. It is shown that for the membrane problems, the generated expressions for the eigenvalues and eigenfunctions are identical with the corresponding exact solutions. For the clamped plate compressed uni-axially or biaxially, problems which are not separable and for which no exact solutions are available, the generated eigenvalues, based on a one term expression for the eigenfunction, are shown to agree very closely with the relevant results found by other investigators. For plate problems which are separable, the method generates the exact eigenvalues and eigenfunctions. It was found that in all treated cases the final results are independent of the initial choice of the functions and that the iterative procedure converges very rapidly. (Author)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL ANALYSIS), MEMBRANES, METAL PLATES, VIBRATION, STABILITY, BUCKLING, BOUNDARY VALUE PROBLEMS, ITERATIONS, CONVERGENCE, APPROXIMATION(MATHEMATICS)

Subject Categories : Theoretical Mathematics
      Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE