Numerical Computation of the Matrix Riccati Equation for Heat Propagation during Space Shuttle Reentry.
Abstract
A computer program named HEATEST required excessive computer time to evaluate the matrix Riccati equation for temperature covariance. Alternative numerical methods were employed to compute the Riccati equation, and the HEATEST program execution time was reduced by 70%. However, cumulative temperature covariance rose from 2.45 to 3.28 degrees. This rise was considered insignificant. A survey was conducted of methods for computing the matrix exponential. A triangular matrix decomposition method proved to be more efficient than summing the Taylor series, especially for matrices with a large condition number. This substitution produced an overall 10% decrease in HEATEST execution time with comparable accuracy. Simpson's Rule was used to evaluate the matrix Riccati integral term. The accuracy of this method was in the range of 5 to 9 significant digits, and computation time for the integral term was reduced by 90% for a matrix of order 13. This substitutuion prompted the rise in the covariance. FORTRAN program modules and numerical examples are included. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1982
- Accession Number
- ADA124873
Entities
People
- Philip Wayne Sagstetter
Organizations
- Air Force Institute of Technology