# A Predictor-Corrector Scheme for Conservation Equations with Discontinuous Coefficients

## DOI:

https://doi.org/10.5614/j.math.fund.sci.2020.52.3.6## Keywords:

discontinuous flux, finite difference approximation, MacCormack scheme## Abstract

In this paper we propose an explicit predictor-corrector finite difference scheme to numerically solve one-dimensional conservation laws with discontinuous flux function appearing in various physical model problems, such as traffic flow and two-phase flow in porous media. The proposed method is based on the second-order MacCormack finite difference scheme and the solution is obtained by correcting first-order schemes. It is shown that the order of convergence is quadratic in the grid spacing for uniform grids when applied to problems with discontinuity. To illustrate some properties of the proposed scheme, numerical results applied to linear as well as non-linear problems are presented.

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