A three-point sixth-order nonuniform combined compact difference scheme

A three-point nonuniform combined compact difference (NCCD) scheme with sixth-order accuracy is proposed for numerical models. The NCCD scheme is a generalization of the previously proposed combined compact difference (CCD) scheme with a global Hermitan polynomial spline and has major improved features such as error and computational (CPU) time reduction. For nonperiodic boundaries, additional sixth- or fifth-order nonuniform boundary conditions are proposed. The NCCD scheme with either sixth- or fifth-order additional boundary conditions can increase the accuracy and decrease the CPU time about 1-2 orders of magnitude, compared to the CCD scheme.