For dynamic traffic assignment problem in road network,we adopt a conserved higher-order (CHO) model for modeling and numerical study. The CHO model is combined with dynamic network loading (DNL) model,and the dynamic network loading model is analyzed through variational inequalities. In numerical simulation,the first-order finite volume method was used to solve the CHO model,and a gradient descent method was used to solve the variational inequality problem of the dynamic network loading model iteratively. Finally,a distribution equilibrium was achieved under the dynamic user optimal condition. The numerical results show that the combination of CHO model and DNL model is feasible for solving the dynamic traffic assignment problem.

We develop a lattice Boltzmann model for compound Burgers-Korteweg-de Vries (cBKdV) equation. By properly treating dispersive term u_xxx and applying Chapman-Enskog expansion, the governing equation is recovered correctly from lattice Boltzmann equation and local equilibrium distribution functions are obtained. Numerical experiments show that our results agree well with exact solutions and have better numerical accuracy compared with previous numerical results. This hence indicates that the model is satisfactory and efficient.

Symplectic Fourier pseudo-spectral integrators for Klein-Gordon-Schrödinger equations(KGS) are investigated.A Hamiltonian formulation is presented.Fourier pseudo-spectral discretization is applied to the space approximation which leads to a finite-dimensional Hamiltonian system.Symplectic integrators,including Störmer/Verlet method and midpoint rule,are adopted in the time direction which leads to symplectic integrators for KGS.It suggests that the Störmer/Verlet method is explicit which can be coded effciently,and the midpoint rule captures mass of the original system exactly.Numerical experiments show that symplectic integrator can simulate various solitary well over a long period.