How Can I Solve a Transport PDE with Numerical Methods and Boundary Conditions?

[macrovue]

Here's my question, friends

I have to define initial and boundary condition for a transport PDE: u_t+x(1-x)u_x=0
with x and t is between [0,1], to solve this equation, what kind of numerical method
and boundary condition do you recommend and why?

What kind of numerical error do you expect?

Detailed explanation will be appreciated in advance.

 

[RedBranchKnight]

Can you provide some more detail? Your question is very general.

For starters, I claim no BC are needed/allowed at x = 0,1.

Sounds like a homework exercise. What is the 'basis' for this PDE?