Numerical methods for the optimal transport problem is an active area of research. Recent work of Kitagawa and Abedin shows that the solution of a time-dependent equation converges exponentially fast as time goes to infinity to the solution of the optimal transport problem. This suggests a fast numerical algorithm for computing optimal maps; we investigate such an algorithm here in the 1-dimensional case. Specifically, we use a finite difference scheme to solve the time-dependent optimal transport problem and carry out an error analysis of the scheme. A collection of numerical examples is also presented and discussed.

翻译：计算最佳运输问题的数字方法是一个活跃的研究领域。北川和阿贝丁最近的工作表明,随着时间流到最佳运输问题解决的无限程度,根据时间决定的方程式的解决方案会以指数速度快速汇合。这意味着计算最佳地图的快速数字算法;我们在一维案例中调查这种算法。具体地说,我们使用一个有限差异方案来解决时间流逝的最佳运输问题,并对方案进行错误分析。还提出并讨论了一系列数字实例。