[hunt_mat]

Suppose I have an equation of the form:

u_t+f(x,u)u_x=0

that cannot be written in conservative form. Can I modify the methods for conservative equations, to write something like:

u_(i+1,j)=(u_(i,j-1)+u_(i,j+1))+f(x_j,u_(i,j))*(dt/dx)*(u_(i,j+1)-u_(i,j))

as an extension of the Lax-Friedrichs method?

[FMDenaro]

Originally Posted by hunt_mat

Suppose I have an equation of the form:

u_t+f(x,u)u_x=0

that cannot be written in conservative form. Can I modify the methods for conservative equations, to write something like:

u_(i+1,j)=(u_(i,j-1)+u_(i,j+1))+f(x_j,u_(i,j))*(dt/dx)*(u_(i,j+1)-u_(i,j))

as an extension of the Lax-Friedrichs method?

Just consider the case of the linear scalar equation. However, your formula is wrong, you have to do a central secondo order derivative in space and you missed the factor 0.5 in the lineare average

[hunt_mat]

Originally Posted by FMDenaro

Just consider the case of the linear scalar equation. However, your formula is wrong, you have to do a central secondo order derivative in space and you missed the factor 0.5 in the lineare average

I agree. Should the method work after that?

[FMDenaro]

Originally Posted by hunt_mat

I agree. Should the method work after that?

I strongly discourage using the non conservative form for non linear equations.
Have a look here:

https://www.researchgate.net/publica...rgers_equation