How Do You Solve a Transport PDE with Initial 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.

 

[TaiwanCountry]

Hi , How do you do ?

you can try this answer.

u=f(lnx -ln(1-x)-t) ln() for natural log.

The method is here
http://en.wikipedia.org/wiki/Method_of_characteristics"


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ROC(Taiwan) is not PRC.

http://en.wikipedia.org/wiki/Taiwan"
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