Asynchronous relaxations for the numerical solution of differential equations by parallel processors

Journal Article · Thu Jan 01 00:00:00 EST 1987 · SIAM J. Sci. Stat. Comput.; (United States)

DOI:https://doi.org/10.1137/0908012· OSTI ID:6394813

Mitra, D

The authors consider asynchronous relaxations for the numerical solution by parallel processors of initial value problems involving a class of ordinary differential equations. The differential equations may be nonlinear, nonautonomous and nonhomogeneous. The proposed algorithms have several advantages in the parallel processing context, and these apply irrespective of the number of processors and the architecture of the computing system. The form of the given equations is as a partitioned system which closely corresponds to the composition of physical systems from subsystems. The algorithms iterate asynchronously on functions. They prove that the computed functions uniformly converge at a geometric rate to the unique solution of the given equations. The assumption on the asynchronous aspects of the algorithm are that delays are uniformly bounded and that a nonstarvation condition applies.

• Research Organization: AT and T Bell Labs., Murray Hill, NJ 07974
• OSTI ID: 6394813
• Journal Information: SIAM J. Sci. Stat. Comput.; (United States), Vol. 8:1
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ARRAY PROCESSORS
ALGORITHMS
DIFFERENTIAL EQUATIONS
PARALLEL PROCESSING
COMPUTER ARCHITECTURE
FUNCTIONS
MATRICES
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
EQUATIONS
MATHEMATICAL LOGIC
PROGRAMMING
990210* - Supercomputers- (1987-1989)