A fourth-order compact ADI method for solving two-dimensional unsteady convection–diffusion problems

The new alternating direction implicit difference methods for solving three-dimensional parabolic equations

“…Recently, there has been a renewed interest in the development and application of compact finite difference methods for the numerical solution of the differential equations [10,19,[11][12][13][14][15][16][17][18]. To obtain satisfactory higher-order numerical results with reasonable computational cost, there have been attempted to develop higher-order compact ADI methods.…”

“…For multidimensional problems, the alternating direction implicit (ADI) schemes are preferred for their unconditional stability and high efficiency. As we known, the ADI schemes [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] are unconditional stable and only need to solve a sequence of tridiagonal linear systems. They are efficient methods to solve parabolic differential equations.…”

Fourth-order compact finite difference methods and monotone iterative algorithms for semilinear elliptic boundary value problems

“…However, higher-order methods derived in this manner not only complicate the formulations near the boundaries but also increase the bandwidth of the resulting coefficient matrix. Motivated by these problems, various higher-order compact finite difference discretization techniques for different equations have been developed (see, e.g., [4][5][6][7][8][9][10][11]). In recent years, there has been growing interest in developing fourth-order compact finite difference methods for elliptic differential equations.…”

Exponential high-order compact scheme on nonuniform grids for the steady MHD duct flow problems with high Hartmann numbers

“…HOC difference schemes have been developed and applied to a variety of elliptic equations, the incompressible Navier-Stokes equations and Stokes problems by many authors [27,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46], because they not only provide accurate numerical results and save computational work, but also are easier to deal with boundary conditions. Although an EHOC scheme has been proposed to solve effectively the MHD duct flow problems with low-to-high Ha in [27] very recently, to the best of authors' knowledge, there is still no any report about the implementation of the HOC difference scheme on non-uniform space grids to solve the MHD duct flow problems.…”