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

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macrovue
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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.
 
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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?
 
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Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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