An extended continuum model considering optimal velocity change with memory and numerical tests

2018 ◽  
Vol 490 ◽  
pp. 774-785 ◽  
Author(s):  
Zhai Qingtao ◽  
Ge Hongxia ◽  
Cheng Rongjun
Keyword(s):  
Continuum Model ◽  
Velocity Change ◽  
Optimal Velocity ◽  
Numerical Tests ◽  
With Memory

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

Nonlinear analysis of an improved continuum model considering headway change with memory

2018 ◽  
Vol 32 (03) ◽  
pp. 1850037 ◽  
Author(s):  
Rongjun Cheng ◽  
Jufeng Wang ◽  
Hongxia Ge ◽  
Zhipeng Li
Keyword(s):  
Energy Consumption ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Linear Stability ◽  
Continuum Model ◽  
Density Wave ◽  
Linear Stability Theory ◽  
Traffic Density ◽  
Neutral Stability ◽  
With Memory

Considering the effect of headway changes with memory, an improved continuum model of traffic flow is proposed in this paper. By means of linear stability theory, the new model’s linear stability with the effect of headway changes with memory is obtained. Through nonlinear analysis, the KdV–Burgers equation is derived to describe the propagating behavior of traffic density wave near the neutral stability line. Numerical simulation is carried out to study the improved traffic flow model, which explores how the headway changes with memory affected each car’s velocity, density and energy consumption. Numerical results show that when considering the effects of headway changes with memory, the traffic jams can be suppressed efficiently. Furthermore, research results demonstrate that the effect of headway changes with memory can avoid the disadvantage of historical information, which will improve the stability of traffic flow and minimize car energy consumption.

The KdV–Burgers equation in a new continuum model with consideration of driverʼs forecast effect and numerical tests

2013 ◽  
Vol 377 (44) ◽  
pp. 3193-3198 ◽  
Author(s):  
Hong-Xia Ge ◽  
Ling-Ling Lai ◽  
Peng-Jun Zheng ◽  
Rong-Jun Cheng
Keyword(s):  
Continuum Model ◽  
Burgers Equation ◽  
Numerical Tests

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.

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