We propose and analyze several finite difference schemes for the Hunter–Saxton equation (HS) ut + uux = 1 2 ∫ x 0 (ux) 2 dx, x > 0, t > 0. This equation has been suggested as a simple model for nematic liquid crystals. We prove that the numerical approximations converge to the unique dissipative solution of (HS), as identified by Zhang and Zheng. A main aspect of the analysis, in addition to th...

In this article, we study the numerical approximation of the solution of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with unbounded time and space-dependent coefficients. The PDE free term and the initial data are also allowed to grow. Under the assumption that the PDE does not degenerate, using the L2 theory of solvability in weighted Sobolev spaces, the PDE...

We develop a new two level finite difference scheme for the 1D Pennes bioheat equation. We further prove that the scheme is stable and convergent unconditionally. Numerical experiments for a skin-heating model are conducted. 2005 Elsevier Inc. All rights reserved. 0096-3003/$ see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.01.052 * Corresponding author. E-mail ad...

In this paper, an unconditionally stable three-dimensional (3-D) finite-difference time-method (FDTD) is presented where the time step used is no longer restricted by stability but by accuracy. The principle of the alternating direction implicit (ADI) technique that has been used in formulating an unconditionally stable two-dimensional FDTD is applied. Unlike the conventional ADI algorithms, ho...

A technique to incorporate directivity in the Pseudospectral time-domain method (PSTD) for auralization purposes is presented. The Pseudospectral time-domain method is a numerical method for solving the wave equation that requires only two spatial points per wavelength, making it more efficient compared to other wave based methods. The effect of source directivity as well as the head-related di...

In view of the insufficiencies of existing research into soil water and heat movements in seasonally frozen soil regions, water–heat coupled movements in seasonally frozen soil were studied by using a numerical simulation method. On the basis of viscous flow theory for liquid water in porous media and the heat balance principle, one-dimensional seasonal frozen soil water–heat coupled movements ...

In this article a numerical method involving classical finite difference scheme on non-uniform grid is constructed for a singularly perturbed convection-diffusion boundary value problem with two small parameters affecting the convection and diffusion terms. The scheme has been analyzed for uniform convergence with respect to both singular perturbation parameters. To support the theoretical erro...

Three-dimensional fluid flow around two circular cylinders in tandem arrangement is computed by the finite difference method without a turbulence model. The overlapped grid technique is employed to catch the flow interference between the two tandem cylinders. It is confirmed that the abrupt numerical change of drag coefficients and the Strouhal number is in good agreement with the previous expe...

We develop a simple energy method for proving the stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems. In particular, we extend to several space dimensions and to variable coefficients a crucial stability result by Goldberg and Tadmor for Dirichlet boundary conditions. This allows us to give some conditions on the discretized operator that ensu...

In this paper scalar and vector data are visualised by suited colour scales based on perceptive and uniform colour models. Using opportune colour scales, colour information is created from the two-dimensional scalar data computed at different time steps. Direction and magnitude of computed vector data are represented employing circular colour look-up tables (LKT). In a scientific computing envi...