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A procedure with stepsize control for solving n one-dimensional IVPs

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  • Salkuyeh, Davod Khojasteh
  • Toutounian, Faezeh
  • Yazdi, Hamed Shariat

Abstract

Finite precision computations may affect the stability of algorithms and the accuracy of computed solutions. In this paper we first obtain a relation for computing the number of common significant digits between the exact solution and a computed solution of a one-dimensional initial-value problem obtained by using a single-step or multi-step method. In fact, by using the approximate solutions obtained with stepsizes h and h /2, the number of common significant digits between approximate solution with stepsize h and exact solution is estimated. Then by using the stochastic arithmetic, the CESTAC method, and the CADNA library we propose an algorithm to control the round-off error effect on the computed solution. This method can easily apply to a system of n one-dimensional initial-value problems. Finally some numerical examples are given to show the efficiency of the method.

Suggested Citation

  • Salkuyeh, Davod Khojasteh & Toutounian, Faezeh & Yazdi, Hamed Shariat, 2008. "A procedure with stepsize control for solving n one-dimensional IVPs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(2), pages 167-176.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:2:p:167-176
    DOI: 10.1016/j.matcom.2007.11.004
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    References listed on IDEAS

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    1. Vignes, J., 1978. "New methods for evaluating the validity of the results of mathematical computations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 20(4), pages 227-249.
    2. Vignes, J., 1993. "A stochastic arithmetic for reliable scientific computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(3), pages 233-261.
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