We develop efficient moving mesh algorithms for oneand two-dimensional hyperbolic systems of conservation laws. The algorithms are formed by two independent parts: PDE evolution andâ€¦ (More)

We introduce a new approach to obtain sharp pointwise error estimates for viscosity approximation (and, in fact, more general approximations) to scalar conservation laws with piecewise smoothâ€¦ (More)

It is proved that for scalar conservation laws, if the flux function is strictly convex, and if the entropy solution is piecewise smooth with finitely many discontinuities (which includes initialâ€¦ (More)

Pseudospectral methods are investigated for singularly perturbed boundary value problems for ordinary diierential equations which possess boundary layers. It is well known that if the boundary layerâ€¦ (More)

In practice, there are three types of adaptive methods using the finite element approach, namely the h-method,p-method, andr-method. In theh-method, the overall method contains two parts, a solutionâ€¦ (More)

In this paper, a Jacobi-collocation spectral method is developed for Volterra integral equations of the second kind with a weakly singular kernel. We use some function transformations and variableâ€¦ (More)

Numerical methods for solving the continuum model of the dynamics of the molecularbeam epitaxy (MBE) require very large time simulation, and therefore large time steps become necessary. The mainâ€¦ (More)

IEEE Transactions on Intelligent Transportationâ€¦

2013

For urban metro systems with platform screen doors, train automatic stop control (TASC) has recently attracted significant attention from both industry and academia. Existing solutions to TASC areâ€¦ (More)