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Intervals of periodicity and absolute stability of explicit nyström methods fory″=f(x,y)

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Abstract

We examine intervals of periodicity and absolute stability of explicit Nyström methods fory″=f(x,y) by applying these methods to the test equationy″=−λ 2 y,λ>0. We consider in detail general families of fourth-order explicit Nyström methods; necessary and sufficient conditions are given to characterize methods which possess non-vanishing intervals of periodicity and absolute stability. We establish closed-form expressions giving intervals of periodicity and/or absolute stability, in case these exist, for any fourth-order method. We then show that the methodM 4 (1/6, 5/6) has the largest interval of periodicity out of all fourth-order methods; we also obtain the fourth-order method with the largest interval of absolute stability. The corresponding results for second and third-order explicit Nyström methods are also included.

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Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, 88003, Las Cruces, New Mexico, USA

    M. M. Chawla & S. R. Sharma

  2. Department of Mathematics, Indian Institute of Technology, Hauz Khaz, 110016, New Delhi, India

    M. M. Chawla & S. R. Sharma

Authors
  1. M. M. Chawla
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  2. S. R. Sharma
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Chawla, M.M., Sharma, S.R. Intervals of periodicity and absolute stability of explicit nyström methods fory″=f(x,y). BIT 21, 455–464 (1981). https://doi.org/10.1007/BF01932842

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  • DOI: https://doi.org/10.1007/BF01932842

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