High-order-accurate discretization of a second-order equation with discontinuous coefficients

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Abstract

A numerical procedure for accurate discretization of a second-order linear differential equation with discontinuous (piecewise continuous) coefficients is developed. Using the original equation, the high-order derivatives of the Taylor series expansion of the truncation error are expressed in terms of the lower order derivatives. The procedure results in a numerical algorithm of high accuracy, O(hm), where h is the grid spacing and m is, in principle, arbitrary. Calculations based on the proposed algorithm were compared with exact analytical results of different examples.

Original languageEnglish
Pages (from-to)69-79
Number of pages11
JournalApplied Mathematical Modelling
Volume22
Issue number1-2
DOIs
StatePublished - 1 Jan 1998

Keywords

  • Discontinuous coefficients
  • Finite-differences
  • High-order scheme
  • Second-order equation

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