Solving transport-density equation with diffusion using the first integral method and the generalized hyperbolic functions method

• Main Author: Moner Soliby, Rfaat
• Format: Thesis
• Language: English; English; English
• Published: 2020
• Subjects: TK7800-8360 Electronics
• Online Access: http://eprints.uthm.edu.my/1113/

This study gives an overview of nonlinear partial differential transport-density equation with diffusion traffic flow model. Basically, the first integral method (FIM) and the generalized hyperbolic functions method (GHFM) are employed to solve the proposed model and to give compelling evidence that regularization of the conservation law by adding viscosity that will undeniably remove the singularity and the weak solution obtained by the characteristic method. As long as, continuity equation leads to discontinuous solutions, abrupt change of the traffic density; thus the diffusion was introduced so as to prevent incrementally deformation of the wave so that shock, rarefication and singularity will not be existed anymore. Subsequently, smooth the resulting density field between the two asymptotic states. On the base of the solution, physical interpretations for some obtained solutions were discussed in order to detect the effects of diffusion on this dynamical traffic flow model.