Hyperbolic systems of partial differential equations are found in modeling separation and reaction engineering problems. They can be divided into linear, semi-linear, quasi-linear and non-linear equations. In this paper two mathematical tools for the solution of PDEs: the numerical method of characteristics and Lax-Wendroff schemes are reviewed and applied to the solution of various problems: fixed-bed reactor for MTBE synthesis (system of semi-linear equations), separation of xylene isomers (reducible system of quasi-linear equations) and adsorptive reactors (non-reducible system of quasi-linear equations).
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