This paper introduces a new perspective of the traditional view on the velocity of each physical particle in the coupled Burgers’ equation in the backward semi-Lagrangian method (BSLM). The proposed methods reduce the number of Cauchy problems to be solved by observing a single virtual characteristic curve with a velocity. This can drastically reduce the computational cost of determining the departure point. Then, we solve the derived system reflected by the single virtual characteristic curve. Moreover, an efficient strategy for the derived linear system of equations is provided. Four examples are tested to demonstrate the adaptability and efficiency of the proposed method. The test results show that the proposed method has third- and fourth-order accuracy in time and space, respectively. In addition, compared with the existing method of solving the problem along two particles with different velocities, we confirm that the proposed method significantly reduces computational cost while maintaining accuracy well.

本文介绍了后向半拉格朗日法（BSLM）中耦合伯格斯方程中每个物理粒子速度的传统观点的新视角。所提出的方法通过观察具有速度的单个虚拟特征曲线来减少要解决的柯西问题的数量。这可以大大减少确定出发点的计算成本。然后，我们对由单个虚拟特征曲线反映的导出系统进行求解。此外，还提供了导出线性方程组的有效策略。通过四个例子的测试来证明该方法的适应性和效率。测试结果表明，该方法在时间和空间上分别具有三阶和四阶精度。此外，