An extended macro model accounting for acceleration changes with memory and numerical tests

2018 ◽  
Vol 506 ◽  
pp. 270-283 ◽  
Author(s):  
Rongjun Cheng ◽  
Hongxia Ge ◽  
Fengxin Sun ◽  
Jufeng Wang
Keyword(s):  
Macro Model ◽  
Numerical Tests ◽  
With Memory

scholarly journals An Improved Macro Model of Traffic Flow with the Consideration of Ramps and Numerical Tests

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Zhongke Shi ◽  
Wenhuan Ai ◽  
Dawei Liu
Keyword(s):  
Traffic Flow ◽  
Phase Plane ◽  
Macro Model ◽  
Traffic Jams ◽  
Numerical Tests ◽  
Stop And Go ◽  
Point Equation ◽  
Improved Model ◽  
The Relationship ◽  
Real Traffic

We present an improved macro model for traffic flow based on the existing models. The equilibrium point equation of the model is obtained. The stop-and-go traffic phenomenon is described in phase plane and the relationship between traffic jams and system instability is clearly shown in the phase plane diagrams. Using the improved model, some traffic phenomena on a highway with ramps are found in this paper. The numerical simulation is carried out to investigate various nonlinear traffic phenomena with a single ramp generated by different initial densities and vehicle generation rates. According to the actual road sections of Xi’an-Baoji highways, the situations of morning peak with several ramps are also analyzed. All these results are consistent with real traffic, which shows that the improved model is reasonable.

Determination of the fractional order in semilinear subdiffusion equations

2020 ◽  
Vol 23 (3) ◽  
pp. 694-722
Author(s):  
Mykola Krasnoschok ◽  
Sergei Pereverzyev ◽  
Sergii V. Siryk ◽  
Nataliya Vasylyeva
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Computational Algorithm ◽  
Optimality Criterion ◽  
Small Time ◽  
Inverse Boundary ◽  
Regularization Scheme ◽  
Numerical Tests ◽  
With Memory

AbstractWe analyze the inverse boundary value-problem to determine the fractional order ν of nonautonomous semilinear subdiffusion equations with memory terms from observations of their solutions during small time. We obtain an explicit formula reconstructing the order. Based on the Tikhonov regularization scheme and the quasi-optimality criterion, we construct the computational algorithm to find the order ν from noisy discrete measurements. We present several numerical tests illustrating the algorithm in action.

scholarly journals A New High-Order Jacobian-Free Iterative Method with Memory for Solving Nonlinear Systems

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2122
Author(s):  
Ramandeep Behl ◽  
Alicia Cordero ◽  
Juan R. Torregrosa ◽  
Sonia Bhalla
Keyword(s):  
Nonlinear Systems ◽  
Iterative Method ◽  
Order Of Convergence ◽  
Recent Literature ◽  
Basin Of Attraction ◽  
Qualitative Behavior ◽  
Order Convergence ◽  
Numerical Tests ◽  
Initial Scheme ◽  
With Memory

We used a Kurchatov-type accelerator to construct an iterative method with memory for solving nonlinear systems, with sixth-order convergence. It was developed from an initial scheme without memory, with order of convergence four. There exist few multidimensional schemes using more than one previous iterate in the very recent literature, mostly with low orders of convergence. The proposed scheme showed its efficiency and robustness in several numerical tests, where it was also compared with the existing procedures with high orders of convergence. These numerical tests included large nonlinear systems. In addition, we show that the proposed scheme has very stable qualitative behavior, by means of the analysis of an associated multidimensional, real rational function and also by means of a comparison of its basin of attraction with those of comparison methods.

A New Macro Model for Traffic Flow on a Highway with Ramps and Numerical Tests

2009 ◽  
Vol 51 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Tang Tie-Qiao ◽  
Huang Hai-Jun ◽  
S.C Wong ◽  
Gao Zi-You ◽  
Zhang Ying
Keyword(s):  
Traffic Flow ◽  
Macro Model ◽  
Numerical Tests

Capito-Lunate Fusion with Memory Staples

2015 ◽  
Vol 04 (S 01) ◽  
Author(s):  
M. Solomons
Keyword(s):  
With Memory
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