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Error Propagation in Dynamic Iterations Applied to Linear Systems of Differential Equations

In: Integral Methods in Science and Engineering

Author

Listed:
  • B. Zubik-Kowal

    (Boise State University, 1910 University Drive)

Abstract

We derive recurrence relations for the errors of dynamic iterations applied to arbitrarily large linear systems of differential equations and address the question of how the physical parameters inherent to these systems influence the convergence of the iterations. The dependence of the recurrence relations on the parameters allows one to conclude and predict how the magnitudes of the parameters slow down or accelerate the rate of convergence. Using the recurrence relations, we conclude that the smaller the magnitudes of the parameters that are multiplied by the previous iterates, the faster the convergence of the dynamic iterations. We also conclude that changes in the magnitude of even a single parameter may lead to changes in the number of iterations needed to get the desired accuracy of numerical approximations. Our theoretical results and predictions are demonstrated by means of numerical experiments.

Suggested Citation

  • B. Zubik-Kowal, 2023. "Error Propagation in Dynamic Iterations Applied to Linear Systems of Differential Equations," Springer Books, in: Christian Constanda & Bardo E.J. Bodmann & Paul J. Harris (ed.), Integral Methods in Science and Engineering, chapter 0, pages 387-400, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-34099-4_31
    DOI: 10.1007/978-3-031-34099-4_31
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