Accession Number : ADA328947

Title :   Using Diagonally Implicit Multistage Integration Methods for Solving Ordinary Differential Equations. Part 2: Implicit Methods.

Descriptive Note : Interim rept. Oct 94-Sep 96,

Corporate Author : NAVAL AIR WARFARE CENTER WEAPONS DIV CHINA LAKE CA

Personal Author(s) : Van Wieren, Jack

PDF Url : ADA328947

Report Date : AUG 1997

Pagination or Media Count : 122

Abstract : New theoretical results for implicit methods of the recently invented and highly promising class of diagonally implicit multistage integration methods (DIMSIMs) are described. Some new A-stable and L-stable methods are derived, and conditions for a method to have an A-stable or L-stable FASAL (First Approximately Same As Last) implementation are derived. New alternative error estimates are proposed and successfully tested. The stability regions for alternative predictor-corrector DIMSIM implementations are derived. Implementation parameters for stiff solvers based on second and fifth order DIMSIMs are derived. Development of prototype stiff solvers of both second and fifth order stiff DIMSIM solvers is described. Results of successful tests on the Prothero-Robinson problem are reported and demonstrate that DIMSIMs may be used to develop efficient stiff solvers.

Descriptors :   *NUMERICAL ANALYSIS, *INTEGRATION, *DIFFERENTIAL EQUATIONS, MATHEMATICAL LOGIC, ESTIMATES, ERROR ANALYSIS, COMPUTER BENCHMARKING.

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE