Abstract
One-Dimensional Explicit Tolesa Numerical Scheme for Solving First Order Hyperbolic Equations and Its Application to Macroscopic Traffic Flow Model
Highlights
Hyperbolic partial differential equation of conservation laws has recently received great attention and many books have been published in this area [1] [2][3] [4]
Macroscopic traffic flow model is first developed by Lighthill Whitham and Richards (LWR) and used to study traffic flow by collective variables such as flow rate, velocity and density
The finite difference approximations of the first order hyperbolic partial differential Equation (1) using one-dimensional explicit numerical schemes are presented in the following subsection
Summary
Hyperbolic partial differential equation of conservation laws has recently received great attention and many books have been published in this area [1] [2]. Having been studied carefully the space and time mesh sizes and patterns or schematic diagrams of all these schemes, another but a new scheme has been developed and named as one-dimensional explicit Tolesa numerical scheme The implication of the advection Equation (1) together with initial value problem in the context of Lighthill Whitham and Richards (LWR) traffic flow model is implemented. The simulations of traffic flow model with constant speed will be done by using the mentioned one-dimensional explicit numerical schemes including Tolesa scheme, and linear density-speed relationship will be simulated by using Tolesa scheme. The finite difference approximations of the first order hyperbolic partial differential equation using one-dimensional explicit numerical schemes are presented.
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