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 language | English |
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Pages (from-to) | 69-79 |
Number of pages | 11 |
Journal | Applied Mathematical Modelling |
Volume | 22 |
Issue number | 1-2 |
DOIs | |
State | Published - 1 Jan 1998 |
Keywords
- Discontinuous coefficients
- Finite-differences
- High-order scheme
- Second-order equation
ASJC Scopus subject areas
- Modeling and Simulation
- Applied Mathematics