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-by-n matrix. 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.

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.

I have a system of first-order nonlinear partial differential equations. $$A(x,t)\frac{\partial u}{\partial t}(x,t) + B(x,t)\frac{\partial u}{\partial x}(x,t) + c(x,t) = 0$$ 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.

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-by-n matrix. 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.