[Math] Methods of characteristic for system of first order linear hyperbolic partial differential equations: reference and examples

Question

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

• Method of characteristics for a system of pdes
• Solving a system of PDEs with method of characteristics

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

• Courant, Methods of Mathematical physics (1962) – Willey & Sons

• Courant and Lax, On nonlinear partial differential equations with two independent variables (1949) (beyond a paywall)

• John, Partial Differential Equations, 3-rd edition (1978) – Springer

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.

Answer 1

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.