We provide a preliminary comparison of the dispersion properties, specifically the time-amplification factor, the scaled group velocity and the error in the phase speed of four spatiotemporal discretization schemes utilized for solving the one-dimensional (1D) linear advection diffusion reaction (ADR) equation: (a) An explicit (RK2) temporal integration combined with the Optimal Upwind Compact Scheme (or OUCS3) and the central difference scheme (CD2) for second order spatial discretization, (b) a fully implicit mid-point rule for time integration coupled with the OUCS3 and the Lele's compact scheme for first and second order spatial discretization, respectively, (c) An implicit (mid-point rule)-explicit (RK2) or IMEX time integration blended with OUCS3 and Lele's compact scheme (where the IMEX time integration follows the same ideology as introduced by Ascher et al.), and (d) the IMEX (mid-point/RK2) time integration melded with the New Combined Compact Difference scheme (or NCCD scheme). Analysis reveal the superior resolution features of the IMEX-NCCD scheme including an enhanced region of neutral stability (a region where the amplification factor is close to one), a diminished region of spurious propagation characteristics (or a region of negative group velocity) and a smaller region of nonzero phase speed error. The dispersion error of these numerical schemes through the role of q-waves is further investigated using the novel error propagation equation for the 1D linear ADR equation. Again, the in silico experiments divulge excellent Dispersion Relation Preservation (DRP) properties of the IMEX-NCCD scheme including minimal dissipation via implicit filtering and negligible unphysical oscillations (or Gibbs' phenomena) on coarser grids.

中文翻译：

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对流扩散反应方程的隐-显-紧缩方法

s 紧凑方案（其中 IMEX 时间积分遵循 Ascher 等人介绍的相同意识形态），以及 (d) IMEX（中点/RK2）时间积分与新组合紧凑差分方案（或 NCCD 方案）融合. 分析揭示了 IMEX-NCCD 方案的卓越分辨率特性，包括增强的中性稳定性区域（放大系数接近 1 的区域）、减少的杂散传播特性区域（或负群速度区域）和非零相位速度误差的较小区域。使用一维线性 ADR 方程的新型误差传播方程进一步研究了通过 q 波作用产生的这些数值方案的色散误差。再次，