ABSTRACT This study presents a three-level explicit time-split MacCormack method to compute approximate solutions of two-dimensional time-dependent linear convection-diffusion-reaction equations with source term. The difference operators split the two-dimensional problem into two pieces so that each subproblem is easily solvable using the original MacCormack approach. Second order accuracy in time and fourth-order convergence in space are achieved by the application of the Taylor series expansion. The proposed algorithm minimizes the computational time, computer memory requirement and is easy to implement. Under a suitable time-step restriction, both stability and error estimates of the numerical scheme are deeply analysed in -norm. Numerical evidences which confirm the theoretical analysis are considered and discussed.

中文翻译：

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具有源项的二维演化线性对流-扩散-反应方程的一种新的三级时分 MacCormack 方案

摘要 本研究提出了一种三级显式时间分割 MacCormack 方法，用于计算具有源项的二维时间相关线性对流-扩散-反应方程的近似解。差分算子将二维问题分成两部分，以便使用原始 MacCormack 方法可以轻松解决每个子问题。时间二阶精度和空间四阶收敛是通过应用泰勒级数展开实现的。所提出的算法最大限度地减少了计算时间和计算机内存需求，并且易于实现。在合适的时间步长限制下，数值方案的稳定性和误差估计都在范数中进行了深入分析。对证实理论分析的数值证据进行了考虑和讨论。