If its not possible, how can i discretize the equation numerically ? I am intrested in finding the variable in next instant based on the previous observations.
In otherwords, I can say that my equation is almost similar to burgers equation. How can I solve analytically or numerically
I have a LWR traffic flow equation in terms of speed as (do 'u'/''do 't') + a(do 'u'/do 'x'), where 'a' is '2u-uf'... and uf is constant and u is a variable.
If I understand your notation, it appears you have a wave-type equation, specifically a variation of Burger's equation without "viscosity". These equations can be solved in closed form (see the fairly good wikipedia article at https://en.wikipedia.org/wiki/Burgers%27_equation, for example). If you really want to do it numerically, there are standard discretization methods, as well. See the very good reference "Computational Fluid Mechanics and Heat Transfer" by Tannehill, et al. They discuss various Burger-type equations extensively and you should easily be able to code-up one of their numerical methods in MATLAB.
Thanks dear Michael..
But How can I solve burger equation which is in conservation form using method of characteristics
The method of characteristics is described in many text-books. You could also take a look on this page http://en.wikipedia.org/wiki/Method_of_characteristics.
The characteristic system for your equation is
dt/1=dx/(2u-uf), its solution is 2u*t-uf*t-x=C, where C is a constant, then the general solution is u=F( 2u*t-uf*t-x), where F is an arbitrary function. Alternatively you can write the solution as phi(u)+ 2u*t - uf*t - x=0, where phi is an arbitary function (MAPLE provides solution in this latter form). So, it is possible to get analytical general solution in an implicit form only. The simple particular solution is u=(x+uf*t)/(2t+c), where c is a constant.
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