The non-reflecting boundary is much more difficult, and two methods are presented here. The first is based on the one way wave equation as derived by factoring the one dimensional wave equation  into two one way wave equations. This assumes the primary wave direction is normal to the boundary. The partial differential operators are factored, and these wave equations propagate in the direction of the sign of Equation 59.
Factoring the operator of the previous equation gives
Now if the product of two terms in Equation 59 is zero, then either term could be zero, and for the left side of the model we have Equation 60: