Numerical Analysis of the Parabolic 1-D Optimal Transport Problem

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