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## Main Question or Discussion Point

I am looking for a method to solve coupled first order PDEs in following

form:

[tex]

\frac {\partial u1} {\partial x} = f(x,t,u1,u2)

[/tex]

[tex]

\frac {\partial u2} {\partial t} = g(x,t,u1,u2)

[/tex]

Subject to prober BC and IC. and consider:

[tex]

u1=F(x,t)

[/tex]

[tex]

u2=G(x,t)

[/tex]

I am looking for both numerical and analytical methods. Please note F and G are both nonlinear and I am not sure if we could find an analytical solution. The method of characteristics can give us a solution for quasi linear and linear sets.

/Mohmmad

form:

[tex]

\frac {\partial u1} {\partial x} = f(x,t,u1,u2)

[/tex]

[tex]

\frac {\partial u2} {\partial t} = g(x,t,u1,u2)

[/tex]

Subject to prober BC and IC. and consider:

[tex]

u1=F(x,t)

[/tex]

[tex]

u2=G(x,t)

[/tex]

I am looking for both numerical and analytical methods. Please note F and G are both nonlinear and I am not sure if we could find an analytical solution. The method of characteristics can give us a solution for quasi linear and linear sets.

/Mohmmad