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The (1+1)D Transmission Line
As a slightly more involved example, which highlights some of the issues which typically arise in the construction of these algorithms, consider the (1+1)D transmission line or telegrapher's equations [63]:
![$\displaystyle \begin{eqnarray}l\frac{\partial i}{\partial t}+\frac{\partial u}{...
...c{\partial u}{\partial t}+\frac{\partial i}{\partial x}+gu+h&=&0 \end{eqnarray}$](img764.png) |
(3.52a) |
Here,
and
are the current and voltage in the transmission line,
,
,
and
are inductance, capacitance, resistance and shunt conductance per unit length respectively, and are all non-negative functions of
(
and
are strictly positive
).
and
represent distributed voltage and current source terms. System (3.56) is symmetric hyperbolic; it has the form of (3.1), with
, and
![$\displaystyle {\bf P} = \begin{bmatrix}l&0\\ 0&c\\ \end{bmatrix}\hspace{0.3in}{...
...0&g\\ \end{bmatrix}\hspace{0.3in}{\bf f} = \begin{bmatrix}e\\ h\\ \end{bmatrix}$](img774.png) |
(3.53) |
Subsections
Stefan Bilbao
2002-01-22