Differential transform method for mathematical modeling of jamming transition problem in traffic congestion flow


== Abstract ==

In this paper we aim to find an analytical solution for jamming transition in traffic flow. Generally the Jamming Transition Problem (JTP) can be modeled via Lorentz system. So, in this way, the governing differential equation achieved is modeled in the form of a nonlinear damped oscillator. In current research the authors utilized the Differential Transformation Method (DTM) for solving the nonlinear problem and compared the analytical results with those ones obtained by the 4th order Runge-Kutta Method (RK4) as a numerical method. Further illustration embedded in this paper shows the ability of DTM in solving nonlinear problems when a so accurate solution is required. In this paper we aim to find an analytical solution for jamming transition in traffic flow. Generally the Jamming Transition Problem (JTP) can be modeled via Lorentz system. So, in this way, the governing differential equation achieved is modeled in the form of a nonlinear damped oscillator. In current research the authors utilized the Differential Transformation Method (DTM) for solving the nonlinear problem and compared the analytical results with those ones obtained by the 4th order Runge-Kutta Method (RK4) as a numerical method. Further illustration embedded in this paper shows the ability of DTM in solving nonlinear problems when a so accurate solution is required.


== Original document ==

The different versions of the original document can be found in:

* [https://vbn.aau.dk/da/publications/a9a322d6-a531-44c4-af78-40cdf2efda5c https://vbn.aau.dk/da/publications/a9a322d6-a531-44c4-af78-40cdf2efda5c]

* [http://link.springer.com/content/pdf/10.1007/s10100-010-0154-7.pdf http://link.springer.com/content/pdf/10.1007/s10100-010-0154-7.pdf],
: [http://link.springer.com/article/10.1007/s10100-010-0154-7/fulltext.html http://link.springer.com/article/10.1007/s10100-010-0154-7/fulltext.html],
: [http://link.springer.com/content/pdf/10.1007/s10100-010-0154-7 http://link.springer.com/content/pdf/10.1007/s10100-010-0154-7],
: [http://dx.doi.org/10.1007/s10100-010-0154-7 http://dx.doi.org/10.1007/s10100-010-0154-7] under the license http://www.springer.com/tdm

* [https://link.springer.com/content/pdf/10.1007%2Fs10100-010-0154-7.pdf https://link.springer.com/content/pdf/10.1007%2Fs10100-010-0154-7.pdf],
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: [https://vbn.aau.dk/en/publications/differential-transform-method-for-mathematical-modeling-of-jammin https://vbn.aau.dk/en/publications/differential-transform-method-for-mathematical-modeling-of-jammin],
: [https://core.ac.uk/display/60455872 https://core.ac.uk/display/60455872],
: [https://dblp.uni-trier.de/db/journals/cejor/cejor20.html#GanjiBID12 https://dblp.uni-trier.de/db/journals/cejor/cejor20.html#GanjiBID12],
: [https://ideas.repec.org/a/spr/cejnor/v20y2012i1p87-100.html https://ideas.repec.org/a/spr/cejnor/v20y2012i1p87-100.html],
: [https://doi.org/10.1007/s10100-010-0154-7 https://doi.org/10.1007/s10100-010-0154-7],
: [https://rd.springer.com/article/10.1007/s10100-010-0154-7 https://rd.springer.com/article/10.1007/s10100-010-0154-7],
: [https://academic.microsoft.com/#/detail/2169164789 https://academic.microsoft.com/#/detail/2169164789]

* [https://vbn.aau.dk/da/publications/a229e24b-9e96-495c-9f74-48f6c050298c https://vbn.aau.dk/da/publications/a229e24b-9e96-495c-9f74-48f6c050298c],
: [https://doi.org/10.1007/s10100-010-0154-7 https://doi.org/10.1007/s10100-010-0154-7],
: [http://www.scopus.com/inward/record.url?scp=84856430706&partnerID=8YFLogxK http://www.scopus.com/inward/record.url?scp=84856430706&partnerID=8YFLogxK]