Convergence and Error Criteria of Iterative Numerical Solutions to the Transient Heat Conduction Equation.
Abstract
Full implicit finite differencing was used to approximate transient heat conduction in two spacial dimensions. The resulting set of linear simultaneous equations was solved using successive over-relaxation iterative methods. Errors between the exact matric solution and the iterated solution were computed and compared with several methods of determining error approximations that use the displacement between iterations and an associated parameter. Fundamental parameters of the iteration matrix, such as the spectral radius, were tested as parameters in the error approximation methods. The error methods were compared with respect to accuracy, ease of computing, and computer resources required. The nodal density used in the numerical approximation to the physical problem was compared with the spectral radius of the resulting iterative matrix problem. The spectral radius increases as nodal density increases. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1982
- Accession Number
- ADA115495
Entities
People
- Robert Alan Warren
Organizations
- Air Force Institute of Technology