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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]:

(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 nonnegative 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

(3.53) 
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Stefan Bilbao
20020122