
Accession Number : AD0761788
Title : Solution of a TwoPoint Boundary Value Problem with Jacobian Matrix Characterized by Extremely Large Eigenvalues,
Corporate Author : RICE UNIV HOUSTON TEX AEROASTRONAUTICS GROUP
Personal Author(s) : Miele,A. ; Aggarwal,A. K. ; Tietze,J. L.
Report Date : 1972
Pagination or Media Count : 31
Abstract : The paper treats the nonlinear, twopoint boundaryvalue problem d squared x/dt squared  k sinh(kx) = 0, x(0) = 0, x(1) = 1 for relatively large values of k, namely, k = 5, k = 6, and k = 10. Computationally speaking, this is an extremely difficult problem, owing to the fact that the Jacobian matrix is characterized by an extremely large positive eigenvalue: for k = 10, the order of magnitude of this positive eigenvalue near the final point is 1,000. The resulting numerical difficulties are reduced by treating the twopoint boundaryvalue problem as a multipoint boundaryvalue problem. The modified quasilinearization algorithm is employed. This is a totally finite difference approach, which bypasses the integration of the nonlinear equations, which characterizes shooting methods. Solutions for x(t) precise to six significant figures are obtained. (Author)
Descriptors : (*BOUNDARY VALUE PROBLEMS, NUMERICAL ANALYSIS), DIFFERENCE EQUATIONS, ITERATIONS, TABLES(DATA), COMPUTER PROGRAMMING, NUMERICAL INTEGRATION
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE