# Accession Number:

## AD0761788

# Title:

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

# Descriptive Note:

# Corporate Author:

## RICE UNIV HOUSTON TEX AERO-ASTRONAUTICS GROUP

# Personal Author(s):

# Report Date:

## 1972-01-01

# Pagination or Media Count:

## 31.0

# Abstract:

The paper treats the nonlinear, two-point boundary-value problem d squared xdt squared - k sinhkx 0, x0 0, x1 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 xt precise to six significant figures are obtained. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics