Abstract
In this paper a new method for obtaining an exact and numerical solution of initial value problem for a first order nonlinear partial equation which describes the traffic flow on highway in a class of discontinuous functions is developed. For this goal, at first, the special auxiliary problem having some advantages over the main problem has been suggested and using the solution of the auxiliary problem an original method for finding the weak solution of the main problem has been suggested. Using the advantages of the auxiliary problem the new numerical method for obtaining a solution which expresses the all physical properties accurately is purposed, too.
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