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TRAFFIC CONGESTION AN INSTABILITY IN A HYPERBOLIC SYSTEM BY
, 2004
"... In this paper we analyze a class of second order traffic models and show these models support stable oscillatory traveling waves typical of the waves observed on a congested roadway. The basic model has trivial or constant solutions where cars are uniformly spaced and travel at a constant equilibri ..."
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In this paper we analyze a class of second order traffic models and show these models support stable oscillatory traveling waves typical of the waves observed on a congested roadway. The basic model has trivial or constant solutions where cars are uniformly spaced and travel at a constant equilibrium velocity that is determined by the car spacing. The stable traveling waves arise because there is an interval of car spacing for which the constant solutions are unstable. These waves consist of a smooth part where both the velocity and spacing between successive cars are increasing functions of a Lagrange mass index. These smooth portions are separated by shock waves that travel at computable negative velocity. 1.
Transient L¹ error estimates for wellbalanced schemes on nonresonant scalar balance laws
, 2013
"... ..."
Research Plan
, 2001
"... INTRODUCTION. J Since the pioneering work of Hopf [12] on the Cauchy problem u t + uu x = u xx ; t > 0; x 2 R; u(x; 0) = u 0 (x); x 2 R; (1) the Burgers equation has served as a paradigm for the development of the theory of shock waves. My research on convectiondiusion equations has been st ..."
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INTRODUCTION. J Since the pioneering work of Hopf [12] on the Cauchy problem u t + uu x = u xx ; t > 0; x 2 R; u(x; 0) = u 0 (x); x 2 R; (1) the Burgers equation has served as a paradigm for the development of the theory of shock waves. My research on convectiondiusion equations has been started to reveal the metastable phenomenon of the Burgers equation which is the transition of the convection dominant stage to the diusion dominant one. This behavior is quantitatively studied in [3] by introducing diusive Nwaves and an asymptotic series representation of the solution. In [5] we show how to control moments of the initial approximation and achieve desired convergence orders. Some of these techniques are applicable to models for roll waves, front p
Instability Of Numerical Schemes For A ConvectionReaction Equation
"... In this report we observe several undesired behaviors of numerical schemes for the Burgers equation with a linear source term. Numerical solutions based on a splitting method are compared to exact solutions of the problem. method. From several examples we observe how some unexpected properties of nu ..."
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In this report we observe several undesired behaviors of numerical schemes for the Burgers equation with a linear source term. Numerical solutions based on a splitting method are compared to exact solutions of the problem. method. From several examples we observe how some unexpected properties of numerical schemes grow and how they can be neutralized. Key words. instability of numerical schemes, convection, reaction, splitting method AMS subject classifications. 65M12, 65M06 1.
unknown title
, 2006
"... www.elsevier.com/locate/jcp Explicit solutions to a convectionreaction equation and defects of numerical schemes q ..."
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www.elsevier.com/locate/jcp Explicit solutions to a convectionreaction equation and defects of numerical schemes q