On solving systems of ordinary differential equations on MIMD-computers. (English. Russian original) Zbl 1141.65054
Cybern. Syst. Anal. 43, No. 2, 303-309 (2007); translation from Kibern. Sist. Anal. 43, No. 2, 175-182 (2007).
Two aspects of solving systems of ordinary differential equations (ODEs) with initial condition are considered. The first aspect is the solution of the ODEs with approximate initial data and a theorem is given which shows the dependence of the solution on the exact data. For the second aspect of parallelism, a parallel computer with distributed memory is assumed and a parallel implementation of solution methods for ODEs in \(C\) and MPI (message passing interface) with a blockwise distribution of the system is described. Runtime experiments are presented for an Adams method, a Gear method and a Runge-Kutta-method for up to 16 processors.
Reviewer: Thomas Rauber (Bayreuth)
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65Y05 | Parallel numerical computation |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65Y10 | Numerical algorithms for specific classes of architectures |
Keywords:
approximate initial data; parallel implementation; numerical examples; Cauchy problem; systems; distributed-memory MIMD computers; parallelizing of computations; Adams method; Gear method; Runge-Kutta-methodReferences:
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