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( h m ), 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.
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