# System of first order PDE

I have a system of first-order nonlinear partial differential equations. $$A(x,t)\frac{\partial u}{\partial t}(x,t) + B(x,t)\frac{\partial u}{\partial x}(x,t) + c(x,t) = 0$$ $$x \in \mathbb{R}, \quad u(x,0) = u_0(x), \quad u(0,t) = \varphi(t)$$ $A$, $B$ are $n \times n$ matrices. How to solve it numerically using matlab? Is there any way to transform it to system of ODEs in general case? Most of the matlab functions(pdepe, pdenonlin) seems to be inappropriate, because they can solve only 2nd order systems.

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Wouldn't the first question be more appropriate on a MATLAB-specific forum? – Federico Poloni Sep 24 '11 at 13:02
I've already posted one on a MATLAB-specific forum. – MaratYV Sep 24 '11 at 13:43

Here, I presume that $A$ and $B$ are $n\times n$ matrices. Even if they are constant, your system can be elliptic (for instance, the Cauchy-Riemann system of holomorphic functions) or hyperbolic (for instance acoustics). If $n\ge3$, it can even be of mixed type, where ellipticity is coupled to hyperbolicity.
$A$ and $B$ are n-by-n matrices. $n \geq 6$. – MaratYV Sep 24 '11 at 13:45