  We construct, analyse and assess various schemes of second order of accuracy
in space and time for model advection-diffusion-reaction differential
equations. The constructed schemes are meant to be of practical use in solving
industrial problems and are derived following two related approaches, namely
ADER and MUSCL-Hancock. Detailed analysis of linear stability and local
truncation error are carried out. In addition, the schemes are implemented and
assessed for various test problems. Empirical convergence rate studies confirm
the theoretically expected accuracy in both space and time.

Numerical Analysis;Numerical Analysis