Some methods of integrating ordinary differential equations on a multiprocessor computer

Journal Article · Tue May 01 04:00:00 EDT 1984 · Cybernetics (Engl. Transl.); (United States)

DOI:https://doi.org/10.1007/BF01068753· OSTI ID:5436964

Molchanov, I N; Geets, E G; Yakovlev, M F

This article examines some methods of solving Cauchy's problems for systems of ordinary differential equations which can be used to solve problems on multiprocessor computers that use the parallel computing process. Estimates are given for the efficiency of parallelism as a function of the number of processors in a multiprocessor computer and of the number of arithmetic operations needed to compute the right-hand parts of the differential equations. The asymptotic limiting coefficients of acceleration are obtained for the solution of a problem on multiprocessor computers relative to a single-processor computer having given parameters. It is assumed that calculations are made on r processors, each of which acts at a speed of v oper/sec and that the rate of exchange between arithmetic processors is equivalent to w oper/sec. It is determined that a shift to parallel calculation does not affect the check on an integration step since the discussed methods for use on single- and multiprocessor computers have approximately the same error characteristics and the stability boundaries of the methods do not differ substantially. The results indicate that an effective gain in the speed of calculations is achieved only when special conversion formulas are utilized for the paralleling algorithms which are oriented towards the parallel processing of data.

• OSTI ID: 5436964
• Journal Information: Cybernetics (Engl. Transl.); (United States), Journal Name: Cybernetics (Engl. Transl.); (United States) Vol. 19:5; ISSN CYBNA
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ACCELERATION
ALGORITHMS
BOUNDARY CONDITIONS
CALCULATION METHODS
CAUCHY PROBLEM
COMPUTERS
DATA COVARIANCES
DATA PROCESSING
DIFFERENTIAL EQUATIONS
DIGITAL COMPUTERS
EFFICIENCY
EQUATIONS
MATHEMATICAL LOGIC
PARALLEL PROCESSING
PROCESSING
PROGRAMMING
STABILITY
VELOCITY