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.

翻译：我们设计、分析和评估各种在空间和时间上达到第二等精确度的计划,用于模型对流-扩散-反应-反应差异方程式,设计这些计划是为了在解决工业问题方面实际发挥作用,并遵循两个相关办法,即ADER和MUSCL-Hancock,对线性稳定性和当地脱轨错误进行了详细分析,此外,还针对各种测试问题实施和评估了这些计划,经验性趋同率研究证实了在时间和时间两方面理论上预期的准确性。