| This thesis develops new schemes to approximate the Convective-Diffusive Equation, using the Modified Equation Approach. The stabilities of the new schemes are examined by the von Neumann and Matrix method. The diffusion and accuracy of a selection of new schemes is also presented, along with the stability and accuracy of several well-known previous schemes for the Convective-Diffusive Equation.;The use of the Modified Equation Approach allows the generation of any number of new schemes. All schemes considered are of the two-level, six-point form. The stability requirements for the general two-level, six-point case are considered, allowing the development of an infinite number of second-order accurate schemes which are unconditionally von Neumann stable. A family of third-order, von Neumann stable schemes is also presented, along with a conditionally stable fourth-order scheme. |
