We derive a family of fourth-order finite difference schemes on the rotated grid for the two-dimensional convection–diffusion equation with variable coefficients. In the case of constant convection coefficients, we present an analytic bound on the spectral radius of the line Jacobi’s...

We present a fourth-order compact finite difference scheme on the face centered cubic (FCC) grids for the numerical solution of the two-dimensional convection diffusion equation. The seven-point formula is defined on a regular hexagon, where the strategy of directional derivative is employed to...

Numerical techniques are proposed to solve a 3D time dependent microscale heat transport equation. A second-order finite difference scheme in both time and space is introduced and the unconditional stability of the finite difference scheme is proved. A computational procedure is designed to...

We develop numerical methods for the computer simulation and modeling of a three dimensional heat transfer problem in biological bodies. The technique is intended for the temperature predications and parameter measurements in thermal medical practices and for the studies of thermomechanical...

A new fourth-order compact difference scheme for the three-dimensional (3D) convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it only requires 15 grid points and that it can be decoupled with two colors. The entire...