I would like to understand a few points on the methods of characteristics used to resolve a system of coupled, linear first order partial differential equation (of the hyperbolic type). Some example of them can be found

on this website for instance.

So do you have any good reference about systems of first-order, coupled partial differential equation resolved via the method of characteristics.

Thanks in advance for any comment which would increase the quality of this question.

UPDATE: I've found some references like

but all discuss the non-linear problem, which obscure the presentation for my purpose. Is there no reference, good introduction to the topic for linear system ? In particular, simple examples would be well appreciated. Thanks in advance.


Here's a good reference I found:

  • E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, DOI 10.1007/b7976-1 2, c Springer-Verlag Berlin Heidelberg 2009

Chapter 2 is what you're looking for. You can find a link online.


I will add a one more:

Partial Differential Equations - Garabedian, John Wiley & Sons Inc., 1st edition, 1964 (there is also a newer edition)


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