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Convergence of a numerical procedure for the solution of a fourth order boundary value problem

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Abstract

The convergence of a proposed second order finite difference method for the determination of an approximate solution of the fourth order differential equationy (4)+fy=g is proved. The matrix associated with the system of linear equations that arises is not even assumed to be monotone, as is often the case in practice. The only requirement is that the functionf(x) be nonnegative. In a typical numerical illustration, the observed maximum errors in absolute value are compared with the respective theoretical error bound for a series of the values of the step size.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Manitoba, Winnipeg, Canada

    Riaz A Usmani

  2. Department of Mathematics and Statistics, University of Pittsburg, Pittsburgh, Pennsylvania, USA

    Martin J Marsden

Authors
  1. Riaz A Usmani
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  2. Martin J Marsden
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Usmani, R.A., Marsden, M.J. Convergence of a numerical procedure for the solution of a fourth order boundary value problem. Proc. Indian Acad. Sci. (Math. Sci.) 88, 21–30 (1979). https://doi.org/10.1007/BF02898331

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  • DOI: https://doi.org/10.1007/BF02898331

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