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Solving Initial Value Problems with a Multiprocessor Code

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Parallel Computing Technologies (PaCT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1662))

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Abstract

The semidicretization of a time-dependent nonlinear partial differential equation leads to a large-scale initial value problem for ordi- nary differential equations which often cannot be solved in a reasonable time on a sequential computer. We investigate in what extent can be practically exploited the idea of parallelism across method in the case of such large problems, and using a distributed computational system.

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References

  1. Bellen, A.: Introduction, International Conference on Parallel Methods for ODEs. The State of the Art, Grado (Italy), 10-13 September 1991. Appl. Numer. Math. 11 (1983) 3–5.

    Google Scholar 

  2. Burrage, K.: Parallel methods for initial value problems, Appl. Num. Math. 11 (1993) 5–45

    Article  MATH  MathSciNet  Google Scholar 

  3. De Meyer, H., Van Daele, M., Vanden Berghe, G.: On the implementation of parallel iterated Runge-Kutta methods on a transputer network. Appl. Numer. Math. 13 (1993) 155–163

    Article  MATH  MathSciNet  Google Scholar 

  4. Iserles, A., NØrsett, S. P.: On the Theory of Parallel Runge-Kutta Methods. IMA J. of Numer. Anal. 10 (1990) 463–488.

    Article  MATH  Google Scholar 

  5. Geist, A., et al., PVM: Parallel Virtual Machine. A Users’ Guide and Tutorial for Networked Parallel Computing (1994), MIT Press.

    Google Scholar 

  6. Ghoshal, S. K., Gupta, M., Rajaraman, V.: A parallel multistep predictor-corrector algorithm for solving ODEs, J. Par. Distr. Comput. 6 (1989) 630–648

    Google Scholar 

  7. Hairer, E., Wanner, G., Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems (1991), Springer Verlag.

    Google Scholar 

  8. Jackson, K. R., NØrsett, S. P.: The potential for parallelism in Runge-Kutta methods. SIAM J. Numer. Anal. 32 (1995) 49–82

    Article  MATH  MathSciNet  Google Scholar 

  9. Kahaner, D. K., Ng, E., Schiesser, W. E., Thompson, S.: Experiments with an ODE solver in the parallel solution of method of lines problems on a shared-memory parallel computer. J. Comput. & Appl. Math. 38 (1991) 231–253

    Article  MATH  Google Scholar 

  10. Lioen, W. M., De Swart, J. J. B., Van der Veen, W. A.: Test Set for IVP Solvers, 1996, Report NM-R9615, CWI Amsterdam, http://dbs.cwi.nl:8080/cwwwi/owa/cwwwi.printreports2?ID=9.

  11. Petcu, D.: Implementation of Some Multiprocessor Algorithms for ODEs using PVM, LNCS 1332: Recent Advances in PVM and MPI, eds. M. Bubak, J. Dongarra, J. Wasniewski, Springer-Verlag, Berlin (1997) 375–383.

    Google Scholar 

  12. Petcu, D.: Parallelism in solving ODEs. Mathematical Monographs 64, Printing House of Western University of Timişoara (1998).

    Google Scholar 

  13. Petcu, D., Drăgan, M.: Designing an ODE solving environment. Proceedings of SciTools’98, LNCS (to appear).

    Google Scholar 

  14. Tam, H. W.: Two-stage parallel methods for the numerical solution of ODEs, SIAM J. Sci. Stat. Comput. 13 (1992) 1062–1084

    Article  MATH  MathSciNet  Google Scholar 

  15. Van der Houwen, P. J.: Parallel step-by-step methods, Appl. Num. Math. 11 (1983) 69–81.

    Article  Google Scholar 

  16. Van der Houwen, P. J., Sommeijer, B. P.: Iterated Runge-Kutta methods on parallel computers. SIAM J. Sci. Stat. Comput. 12 (1991) 1000–1028

    Article  MATH  Google Scholar 

  17. Vanderwalle, S., Piessens, R.: Numerical experiments with nonlinear waveform relaxation on a parallel processor. Appl. Num. Math. 8 (1991) 149–161

    Article  Google Scholar 

  18. Xiao-Qiu, S., De-Gui, L., Zhao-Ding, Y.: Some kinds of parallel Runge-Kutta methods, J. Comput. Math., Suppl. Issue (1992) 79–85.

    Google Scholar 

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© 1999 Springer-Verlag Berlin Heidelberg

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Petcu, D. (1999). Solving Initial Value Problems with a Multiprocessor Code. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 1999. Lecture Notes in Computer Science, vol 1662. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48387-X_47

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  • DOI: https://doi.org/10.1007/3-540-48387-X_47

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66363-8

  • Online ISBN: 978-3-540-48387-8

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