Bi-directional delay line
Encyclopedia
In mathematics
, a bi-directional delay line is a numerical analysis
technique used in computer simulation
for solving ordinary differential equation
s by converting them to hyperbolic equations. In this way an explicit solution scheme is obtained with highly robust numerical properties. It was introduced by Auslander in 1968.
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 (Krus et. al. 1990).
It is also known as the transmission line
method TLM
from an independent development by Johns and O'Brian 1980. This is also extended to partial differential equations.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a bi-directional delay line is a numerical analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
technique used in computer simulation
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...
for solving ordinary differential equation
Ordinary differential equation
In mathematics, an ordinary differential equation is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable....
s by converting them to hyperbolic equations. In this way an explicit solution scheme is obtained with highly robust numerical properties. It was introduced by Auslander in 1968.
It originates from simulation of hydraulic pipelines where wave propagation
Wave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
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
HOPSAN
Hopsan is a free simulation environment for fluid and mechatronic systems, developed at Linköping University. Although originally developed for simulation of fluid power systems, it has also been adopted for other domains such as electric power, flight dynamics, and vehicle dynamics...
simulation package (Krus et. al. 1990).
It is also known as the transmission line
Transmission line
In communications and electronic engineering, a transmission line is a specialized cable designed to carry alternating current of radio frequency, that is, currents with a frequency high enough that its wave nature must be taken into account...
method TLM
TLM
TLM may refer to:* Torch Le Monde* Télé Lyon Métropole, TV Channel of Lyon's agglomeration* The Leprosy Mission* The Little Mermaid* Transaction-level modeling* Traditional Latin Mass* Transmission line matrix method* Transmission line measurement...
from an independent development by Johns and O'Brian 1980. This is also extended to partial differential equations.