Semi-Extrapolated Finite Difference Schemes: Stability and Accuracy

Compared to analogous explicit finite difference schemes, semi-extrapolated finite difference schemes exhibit extended stability ranges. Furthermore, because semi-extrapolated schemes are explicit, they are significantly cheaper to use than their implicit counterparts. However, semi-extrapolation can have unexpected effects on accuracy and consistency. In this presentation, the concept of semi-extrapolation will be introduced and semi-extrapolated discretizations of the Advection Equation, Heat Equation, and Advection-Diffusion Equation will be discussed. Then, the semi-extrapolated schemes’ stability constraints for the Advection Equation and Heat Equation will be compared to the corresponding stability constraints of common finite difference schemes. Following this one-dimensional stability analysis will be an overview of the effects semi-extrapolation can have on consistency and accuracy. Time permitting, preliminary stability constraints for the Advection-Diffusion Equation will be presented.