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Difference Scheme on a Uniform Grid for the Singularly Perturbed Cauchy Problem

We consider the Cauchy problem for a singularly perturbed second order ordinary differential equation. Based on the maximum principle, we estimate the solution and its derivatives. We construct an exponential fitted scheme generalizing the well-known scheme due to A. M. Il’in. We also prove the uniform convergence with the first order accuracy and illustrate the results by numerical experiments. Bibliography: 8 titles.

References

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Correspondence to A. I. Zadorin.

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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 11, No. 3, 2011, pp. 114-122.

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Zadorin, A.I., Tikhovskaya, S.V. Difference Scheme on a Uniform Grid for the Singularly Perturbed Cauchy Problem. J Math Sci 195, 865–872 (2013). https://doi.org/10.1007/s10958-013-1625-x

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  • DOI: https://doi.org/10.1007/s10958-013-1625-x

Keywords

  • Boundary Layer
  • Cauchy Problem
  • Maximum Principle
  • Uniform Convergence
  • Uniform Grid