| Abstract: | A fully discrete methodology is investigated from which two-level, explicit, arbitrary-order, conservative numerical schemes for a model parabolic equation can be derived. To illustrate this, fully discrete three-, five-, seven- and nine-point conservative numerical schemes are presented, revealing that a higher-order scheme has a better stability condition. A method from which high-order numerical schemes for a scalar advection-diffusion equation can be developed is discussed. This method is based on high-order schemes of both the advection and diffusion equations. |
