Finding the location of the shock wave of traffic flow on highways in a class of discontinuous functions


WSEAS Transactions on Mathematics, vol.5, no.12, pp.1343-1346, 2006 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 12
  • Publication Date: 2006
  • Journal Name: WSEAS Transactions on Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.1343-1346
  • Keywords: Auxiliary problem, Differences scheme in a class of discontinuous functions, Extended solution, Traffic flow
  • Istanbul Medipol University Affiliated: Yes


In this paper, a method for obtaining an exact solution and the location of the jump in the solution of the Cauchy problem for a first order partial differential equation which describes the traffic flow on highways is suggested. At first, a special auxiliary problem having some advantages over the main problem has been proposed and using the advantages of the auxiliary problem an original method for obtaining the weak solution of the main problem has been proposed. In order to show the effectiveness of the suggested method, on the basis of the real data some numerical experiments have been carried out.