A Three-Point Combined Compact Difference Scheme

A new three-point combined compact difference (CCD) scheme is developed for numerical models. The major features of the CCD scheme are: three point, implicit, sixth-order accuracy, and inclusion of boundary values. Due to its combination of the first and second derivatives, the CCD scheme becomes more compact and more accurate than normal compact difference schemes. The efficient twin-tridiagonal (for calculating derivatives) and triple-tridiagonal (for solving partial difference equation with the CCD scheme) methods are also presented. Besides, the CCD scheme has sixth-order accuracy at periodic boundaries and fifth-order accuracy at nonperiodic boundaries. The possibility of extending to a three-point eighth-order scheme is also included.