The paper rewrites the traffic flow macro models in the form of system of quasilinear hyperbolic partial differential equation of first order, and classifies the models in terms of the coefficient in the equation.
In this paper we constructed two splitting-up schemes by using Hermite method in space directions and replacing derivative by difference quotiests in time direction for hyperbolic partial differential equation ~2u/ t~2=A(x,t)( ~2u/ x~2)+C(y,t)( ~2u/ y~2)+2D(x,t)( u/ u+2E(y,t)( u/ y)+2F(t)u+r(x,y,t), and discussed its stabity and analyzed its accuracy, Finally, a numerical example was given. Namerical results showed that the two differene schemes constructed by the author are better than Lee's schemes.
Compared with conventional simulation,the boundary conditions for solving the second order hyperbolic partial differential equations change greatly,which is the most difficult and crucial point in fuel system research.
On the basis of physical considerations and computational experience, it is poin-ted out that the initial value problem of the Maxwell equations as a set of first order hyperbolic differential equations could become an effective numerical method for the solution of antenna radiation fields.
In this paper the author considers a class of delay hyperbolic differential equations, Oscillation criteria are obtained for the solutions of the equation.
The pseudo-compressibility term is introduced to the continuity equation of incompressible governing equations, which results in a closed hyperbolic system of equations.
We consider viscosity and dispersion regularizations of the nonlinear hyperbolic partial differential equation (ut+uux)x=1/2ux2 with the simplest initial data such that ux blows up in finite time.
Using the invariant measures of homeomorphisms, we study in this paper the asymptotic behavior of the energy E(t) of an hyperbolic partial differential equation in amoving domain.
Finite part integrals introduced by Hadamard in connection with hyperbolic partial differential equations, have been useful in a number of engineering applications.
Coupling the continuity and momentum equations yields a group of quasilinear hyperbolic partial differential equations which can be solved numerically by using the method of characteristics.
For the formal presentation about the definite problems of ultra-hyperbolic equations, the famous Asgeirsson mean value theorem has answered that Cauchy problems are ill-posed to ultra-hyperbolic partial differential equations of the second-order.
It is found that the three-dimensional boundary-layer equations in the vicinity of the zero skin-friction point are reduced to a single nonlinear partial differential equation of hyperbolic type which governs the longitudinal skin-friction component.