# Bi-directional delay line

- Bi-directional delay line
In mathematics, a **bi-directional delay line** is a numerical analysis technique used in computer simulation for solving ordinary differential equations by converting them to hyperbolic equations. In this way an explicit solution scheme is obtained with highly robust numerical properties.

It originates from simulation of hydraulic pipelines where wave propagation was studied. It was then found that it could be used as an efficient numerical technique for numerically insulating different parts of a simulation model in each times step. It is used in the HOPSAN simulation package.

There is an independent development of this in the "transmission line method" TLM, which is also extended to partial differential equations.

**References**

*D.M. Auslander, "Distributed System Simulation with Bi-Directional Delay Line Models", "Journal of Basic Engineering, Trans. ASME p195-p200. June 1968."

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