Accession Number : AD0761788

Title :   Solution of a Two-Point Boundary Value Problem with Jacobian Matrix Characterized by Extremely Large Eigenvalues,

Corporate Author : RICE UNIV HOUSTON TEX AERO-ASTRONAUTICS 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, two-point boundary-value 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 two-point boundary-value problem as a multipoint boundary-value 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